Showing 1–50 of 156 results for author: Ortiz, G

Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles

Authors: Arkadiusz Bochniak, Shinsei Ryu, Jürgen Fuchs, Gerardo Ortiz

Abstract: Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the "DNA" of candidate many-body wave functions - that is, the pattern of dominant orbital occupations restricted to a finite number of lowest Landau levels - we propose… ▽ More Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the "DNA" of candidate many-body wave functions - that is, the pattern of dominant orbital occupations restricted to a finite number of lowest Landau levels - we propose a combinatorial framework that derives these fusion rules directly from microscopic data. By extending Schrieffer's counting argument and introducing classes of topological excitations, our framework provides a unified route to the fusion rules for both Abelian and non-Abelian excitations. This approach elucidates the emergence of topological features from first principles in both fermionic and bosonic systems. △ Less

Submitted 14 May, 2026; v1 submitted 16 April, 2026; originally announced April 2026.

A Minimal Network of Brain Dynamics: Hierarchy of Approximations to Quasi-critical Neural Network Dynamics

Authors: Jeremy B. Goetz, Naruepon Weerawongphrom, Rashid V. Williams-García, John M. Beggs, Gerardo Ortiz

Abstract: We present an interacting model of neural network dynamics that incorporates key biological features, including multiple forms of inhibitory interactions. We develop a hierarchy of analytical mean-field approximations to characterize nonequilibrium phase transitions between ordered, disordered, and chaotic regimes, complemented by a detailed stability analysis. We show that inhibition generically… ▽ More We present an interacting model of neural network dynamics that incorporates key biological features, including multiple forms of inhibitory interactions. We develop a hierarchy of analytical mean-field approximations to characterize nonequilibrium phase transitions between ordered, disordered, and chaotic regimes, complemented by a detailed stability analysis. We show that inhibition generically enhances the stability of network dynamics. The model is consistent with the quasi-criticality hypothesis, exhibiting regions of maximal dynamical susceptibility and mutual information, modulated by the strength of external stimuli. We further demonstrate that, at the mean-field level, the critical transition belongs to the mean-field directed percolation universality class, in agreement with prior experimental and theoretical studies. More broadly, our framework may offer insights into neurological disorders, with the unstable regime exhibiting chaotic dynamics that may be associated with epileptic seizures. △ Less

Submitted 15 July, 2026; v1 submitted 26 December, 2025; originally announced December 2025.

Comments: 27 pages, 21 figures

Algebraic Fusion in a (2+1)-dimensional Lattice Model with Generalized Symmetries

Authors: Chinmay Giridhar, Philipp Vojta, Zohar Nussinov, Gerardo Ortiz, Andriy H. Nevidomskyy

Abstract: The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's original paradigm. Here, we develop an algebraic framework for systematically deriving the fusion rules of topological defects in higher-dimensional lattice sys… ▽ More The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's original paradigm. Here, we develop an algebraic framework for systematically deriving the fusion rules of topological defects in higher-dimensional lattice systems with non-invertible generalized symmetries, and focus on a (2+1)-dimensional quantum Ising plaquette model as a concrete illustration. We show that bond-algebraic automorphisms, when combined with the so-called half-gauging procedure, reveal the structure of the non-invertible duality symmetry operators, which can be explicitly represented as a sequential quantum circuit. The resulting duality defects are constrained by the model's rigid higher symmetries (lower-dimensional subsystem symmetries), leading to restricted mobility. We establish the fusion algebra of these defects. Finally, in constructing the non-invertible duality transformation, we explicitly verify that it acts as a partial isometry on the physical Hilbert space, thereby satisfying a recent generalization of Wigner's theorem applicable to non-invertible symmetries. △ Less

Submitted 24 December, 2025; originally announced December 2025.

Comments: 25 pages, 20 figures

Band Alignment Tuning from Charge Transfer in Epitaxial SrIrO$_3$/SrCoO$_3$ Superlattices

Authors: Jibril Ahammad, Brian B. Opatosky, Tanzila Tasnim, John W. Freeland, Gabriel Calderon Ortiz, Jinwoo Hwang, Gaurab Rimal, Boris Kiefer, Ryan B. Comes

Abstract: Understanding charge transfer at oxide interfaces is crucial for designing materials with emergent electronic and magnetic properties, especially in systems where strong electron correlations and spin-orbit coupling coexist. SrIrO$_3$/SrCoO$_3$ (SIO/SCO) superlattices offer a unique platform to explore these effects due to their contrasting electronic structures and magnetic behaviors. Building on… ▽ More Understanding charge transfer at oxide interfaces is crucial for designing materials with emergent electronic and magnetic properties, especially in systems where strong electron correlations and spin-orbit coupling coexist. SrIrO$_3$/SrCoO$_3$ (SIO/SCO) superlattices offer a unique platform to explore these effects due to their contrasting electronic structures and magnetic behaviors. Building on past theory based on continuity of O 2p band alignment, we employ density functional theory (DFT) to model electron transfer from Ir to Co across the SIO/SCO interface. To characterize these effects, we synthesized epitaxial SIO/SCO superlattices via molecular beam epitaxy. Structural and transport measurements confirmed high crystallinity, metallic behavior, and suppression of Kondo scattering that has been reported in uniform SIO films. Further characterization via X-ray absorption spectroscopy (XAS) revealed orbital anisotropy and valence changes consistent with interfacial charge transfer. Co K- and L$_{2,3}$-edge and Ir L$_2$-edge spectra verified electron donation from Ir to Co, stabilizing the perovskite SCO phase and tuning the electronic structure of SIO via hole-doping. O K-edge XAS showed band alignment shifts in the SIO layer consistent with DFT predictions. Our work here provides a pathway for engineering oxide heterostructures with tailored magnetic and electronic properties. △ Less

Submitted 6 November, 2025; originally announced November 2025.

Comments: 17 pages, 5 figures; Supplementary information: 9 pages, 9 figures

Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases

Authors: Santhosh M, Jorge Dukelsky, Gerardo Ortiz

Abstract: We present and analyze an exactly solvable interacting fermionic pairing model, which features interactions that entangle states at momenta $\mathbf{k}$ and $-\mathbf{k}$. These interactions give rise to novel correlated ground states, leading to a rich phase diagram that includes superconducting, multiple metallic, and Mott-insulating phases. At finite interaction strengths, we observe the emerge… ▽ More We present and analyze an exactly solvable interacting fermionic pairing model, which features interactions that entangle states at momenta $\mathbf{k}$ and $-\mathbf{k}$. These interactions give rise to novel correlated ground states, leading to a rich phase diagram that includes superconducting, multiple metallic, and Mott-insulating phases. At finite interaction strengths, we observe the emergence of multiple many-body Fermi surfaces, which violate Luttinger's theorem and challenge the conventional Landau-Fermi liquid paradigm. A distinguishing feature of our model is that it remains quantum integrable, even with the addition of pairing interactions of various symmetries, setting it apart from the Hatsugai-Kohmoto model. Our results provide an analytically tractable framework for studying strong correlation effects that give rise to fractionalized excitations and unconventional superconductivity, offering valuable insights into a broad class of integrable many-body systems. △ Less

Submitted 5 January, 2026; v1 submitted 12 October, 2025; originally announced October 2025.

Comments: 25 pages, 12 figures, To appear in Physical Review B

Journal ref: Phys. Rev. B 113, 014514 (2026)

Generalized Wigner theorem for non-invertible symmetries

Authors: Gerardo Ortiz, Chinmay Giridhar, Philipp Vojta, Andriy H. Nevidomskyy, Zohar Nussinov

Abstract: We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or antiunitary transformations. Relinquishing an implicit assumption of invertibility, we demonstrate that the fundamental invariance of quantum transition probab… ▽ More We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or antiunitary transformations. Relinquishing an implicit assumption of invertibility, we demonstrate that the fundamental invariance of quantum transition probabilities under the application of symmetries mandates that all non-invertible symmetries may only correspond to {\it projective} unitary or antiunitary transformations, i.e., {\it partial isometries}. This extends the notion of physical states beyond conventional rays in Hilbert space to equivalence classes in an {\it extended, gauged Hilbert space}, thereby broadening the traditional understanding of symmetry transformations in quantum theory. Our generalized theorem applies irrespective of the origin of the (non)invertible symmetry, holds in arbitrary spatial dimensions, and is independent of the Hamiltonian or action. We explore its physical consequences and, using simple model systems, illustrate how the distinction between invertible and non-invertible symmetries can sometimes be tied to the choice of boundary conditions. △ Less

Submitted 25 March, 2026; v1 submitted 29 September, 2025; originally announced September 2025.

Comments: 8 pages, 2 Appendices. As will appear in Phys. Rev. B

Toward a Physics of Deep Learning and Brains

Authors: Arsham Ghavasieh, Meritxell Vila-Minana, Akanksha Khurd, John Beggs, Gerardo Ortiz, Santo Fortunato

Abstract: Deep neural networks and brains both learn and share superficial similarities: processing nodes are likened to neurons and adjustable weights are likened to modifiable synapses. But can a unified theoretical framework be found to underlie them both? Here we show that the equations used to describe neuronal avalanches in living brains can also be applied to cascades of activity in deep neural netwo… ▽ More Deep neural networks and brains both learn and share superficial similarities: processing nodes are likened to neurons and adjustable weights are likened to modifiable synapses. But can a unified theoretical framework be found to underlie them both? Here we show that the equations used to describe neuronal avalanches in living brains can also be applied to cascades of activity in deep neural networks. These equations are derived from non-equilibrium statistical physics and show that deep neural networks learn best when poised between absorbing and active phases. Because these networks are strongly driven by inputs, however, they do not operate at a true critical point but within a quasi-critical regime -- one that still approximately satisfies crackling noise scaling relations. By training networks with different initializations, we show that maximal susceptibility is a more reliable predictor of learning than proximity to the critical point itself. This provides a blueprint for engineering improved network performance. Finally, using finite-size scaling we identify distinct universality classes, including Barkhausen noise and directed percolation. This theoretical framework demonstrates that universal features are shared by both biological and artificial neural networks. △ Less

Submitted 26 September, 2025; originally announced September 2025.

Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models

Authors: Xingzhi Wang, Zohar Nussinov, Gerardo Ortiz

Abstract: Physical systems defined on hyperbolic lattices may exhibit phases of matter that only emerge due to negative curvature. We focus on the case of the Ising model under open boundary conditions and show that an ``intermediate'' phase emerges in addition to standard (high-temperature) paramagnetic and (low-temperature) ferromagnetic phases. When performing the Kramers-Wannier duality the fact that it… ▽ More Physical systems defined on hyperbolic lattices may exhibit phases of matter that only emerge due to negative curvature. We focus on the case of the Ising model under open boundary conditions and show that an ``intermediate'' phase emerges in addition to standard (high-temperature) paramagnetic and (low-temperature) ferromagnetic phases. When performing the Kramers-Wannier duality the fact that it alters boundary conditions becomes crucial, since a finite fraction of lattice sites lie on the boundary. We propose to characterize this ``intermediate'' phase by its sensitivity to boundary conditions, wherein bulk ordering is not spontaneous but rather induced by boundary effects, setting it apart from the Landau paradigm of spontaneous symmetry breaking. By developing a $\mathbb{Z}_2$ symmetry restricted extension of the Corner Transfer Matrix Renormalization Group method, we provide numerical evidence for the existence of all three distinct phases and their corresponding two-stage phase transitions, thereby establishing the complete phase diagram. We also establish how the (spontaneous) intermediate-to-ferromagnetic and the (induced) paramagnetic-to-intermediate transition points are related by the Kramers-Wannier duality relation. We discuss a holographic correspondence between boundary and bulk behaviors and derive exact expressions for boundary correlation functions on Cayley trees. △ Less

Submitted 13 August, 2025; v1 submitted 28 July, 2025; originally announced July 2025.

Comments: 19 pages, 15 figures, Added a discussion about Holography

Journal ref: Phys. Rev. B 112, 214102 (2025)

The Physics of Local Optimization in Complex Disordered Systems

Authors: Mutian Shen, Gerardo Ortiz, Zhiqiao Dong, Martin Weigel, Zohar Nussinov

Abstract: Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e., the complexity of predicting local properties of the solution from local information, for the ground-state problem of both P- and NP-hard spin-glasses and relat… ▽ More Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e., the complexity of predicting local properties of the solution from local information, for the ground-state problem of both P- and NP-hard spin-glasses and related frustrated spin systems. Depending on the model considered, we observe varying scaling behaviors in how errors associated with local predictions decay as a function of the size of the solved subsystem. These errors are intimately connected to global critical threshold instabilities, characterized by gapless, avalanche-like excitations that follow scale-invariant size distributions. Away from criticality, local solvers quickly achieve high accuracy, aligning closely with the results of the computationally much more expensive global minimization. We leverage these findings to introduce a heuristic contraction-based algorithm for globally studying spin-glass ground states. The local solvers further display sharp imprints of the phase transition from the spin-glass to the ferromagnetic phase as the distribution of spin-glass couplings is shifted, as well as characteristic differences for the infinite-range model, implying the existence of specific classes of local hardness. Our findings shed light on how Nature may operate solely through local actions at her disposal. △ Less

Submitted 23 December, 2025; v1 submitted 5 May, 2025; originally announced May 2025.

Comments: 9+21 pages, 8+24 figures. Add 8 figures

Thermal Annealing and Radiation Effects on Structural and Electrical Properties of NbN/GaN Superconductor/Semiconductor Junction

Authors: Stephen Margiotta, Binzhi Liu, Saleh Ahmed Khan, Gabriel Calderon Ortiz, Ahmed Ibreljic, Jinwoo Hwang, A F M Anhar Uddin Bhuiyan

Abstract: In the rapidly evolving field of quantum computing, niobium nitride (NbN) superconductors have emerged as integral components due to their unique structural properties, including a high superconducting transition temperature (Tc), exceptional electrical conductivity, and compatibility with advanced device architectures. This study investigates the impact of high-temperature annealing and high-dose… ▽ More In the rapidly evolving field of quantum computing, niobium nitride (NbN) superconductors have emerged as integral components due to their unique structural properties, including a high superconducting transition temperature (Tc), exceptional electrical conductivity, and compatibility with advanced device architectures. This study investigates the impact of high-temperature annealing and high-dose gamma irradiation on the structural and superconducting properties of NbN films grown on GaN via reactive DC magnetron sputtering. The as-deposited cubic δ-NbN (111) films exhibited a high-intensity XRD peak, high Tc of 12.82K, and an atomically flat surface. Annealing at 500 and 950 °C for varying durations revealed notable structural and surface changes. High-resolution STEM indicated improved local ordering, while AFM showed reduced surface roughness after annealing. XPS revealed a gradual increase in the Nb/N ratio with higher annealing temperatures and durations. High-resolution XRD and STEM analyses showed lattice constant modifications in δ-NbN films, attributed to residual stress changes following annealing. Additionally, XRD phi-scans revealed sixfold symmetry in NbN films due to rotational domains relative to GaN. While Tc remained stable after annealing at 500 °C, increasing the annealing temperature to 950 °C degraded Tc to ~8K and reduced the residual resistivity ratio from 0.85 in as-deposited films to 0.29 after 30 minutes. The effects of gamma radiation (5 Mrad (Si)) were also studied, demonstrating minimal changes to crystallinity and superconducting performance, indicating excellent radiation resilience. These findings highlight the potential of NbN superconductors for integration into advanced quantum devices and their suitability for applications in radiation-intensive environments such as space, satellites, and nuclear power plants. △ Less

Submitted 28 May, 2025; v1 submitted 13 January, 2025; originally announced January 2025.

Journal ref: J. Vac. Sci. Technol. A 43, 042701 (2025)

Heterostructure and Interfacial Engineering for Low-Resistance Contacts to Ultra-Wide Bandgap AlGaN

Authors: Yinxuan Zhu, Andrew A. Allerman, Chandan Joishi, Jonathan Pratt, Agnes Maneesha Dominic Merwin Xavier, Gabriel Calderon Ortiz, Brianna A. Klein, Andrew Armstrong, Jinwoo Hwang, Siddharth Rajan

Abstract: We report on the heterostructure and interfacial engineering of metalorganic chemical vapor deposition (MOCVD) grown reverse-graded contacts to ultra-wide bandgap AlGaN. A record low contact resistivity of 1.4 x 10-6 Ohm.cm2 was reported on an Al0.82Ga0.18N metal semiconductor field effect transistor (MESFET) by compositionally grading the contact layer from Al0.85Ga0.15N to Al0.14Ga0.86N with deg… ▽ More We report on the heterostructure and interfacial engineering of metalorganic chemical vapor deposition (MOCVD) grown reverse-graded contacts to ultra-wide bandgap AlGaN. A record low contact resistivity of 1.4 x 10-6 Ohm.cm2 was reported on an Al0.82Ga0.18N metal semiconductor field effect transistor (MESFET) by compositionally grading the contact layer from Al0.85Ga0.15N to Al0.14Ga0.86N with degenerate doping and proper interfacial engineering considering bandgap-narrowing-induced band offset between channel and contact layer. This represents orders-of-magnitude of lower contact resistivity than that obtained in similar MOCVD-grown structures. A detailed, layer-by-layer analysis of the reverse graded contact and TCAD simulation of the bandgap narrowing effect highlighted that the reverse graded contact layer itself is extremely conductive and interfacial resistance due to bandgap-narrowing-induced barrier between contact and channel dominates the contact resistance. △ Less

Submitted 15 November, 2024; originally announced November 2024.

Unconventional Unidirectional Magnetoresistance in vdW Heterostructures

Authors: I-Hsuan Kao, Junyu Tang, Gabriel Calderon Ortiz, Menglin Zhu, Sean Yuan, Rahul Rao, Jiahan Li, James H. Edgar, Jiaqiang Yan, David G. Mandrus, Kenji Watanabe, Takashi Taniguchi, Jinwoo Hwang, Ran Cheng, Jyoti Katoch, Simranjeet Singh

Abstract: Electrical readout of magnetic states is a key to realize novel spintronics devices for efficient computing and data storage. Unidirectional magnetoresistance (UMR) in bilayer systems, consisting of a spin source material and a magnetic layer, refers to a change in the longitudinal resistance upon the reversal of magnetization, which typically originates from the interaction of spin-current and ma… ▽ More Electrical readout of magnetic states is a key to realize novel spintronics devices for efficient computing and data storage. Unidirectional magnetoresistance (UMR) in bilayer systems, consisting of a spin source material and a magnetic layer, refers to a change in the longitudinal resistance upon the reversal of magnetization, which typically originates from the interaction of spin-current and magnetization at the interface. Because of UMR s linear dependence on applied charge current and magnetization, it can be used to electrically read the magnetization state. However, in conventional spin source materials, the spin polarization of an electric field induced spin current is restricted to be in the film plane and hence the ensuing UMR can only respond to the in plane component of the magnetization. On the other hand, magnets with perpendicular magnetic anisotropy (PMA) are highly desired for magnetic memory and spin-logic devices, while the electrical read out of PMA magnets through UMR is critically missing. Here, we report the discovery of an unconventional UMR in bilayer heterostructures of a topological semimetal (WTe2) and a PMA ferromagnetic insulator (Cr2Ge2Te6, CGT), which allows to electrically read the up and down magnetic states of the CGT layer by measuring the longitudinal resistance. Our theoretical calculations based on a tight binding model show that the unconventional UMR originates from the interplay of crystal symmetry breaking in WTe2 and magnetic exchange interaction across the WTe2 and CGT interface. Combining with the ability of WTe2 to obtain magnetic field free switching of the PMA magnets, our discoveries open an exciting pathway to achieve two terminal magnetic memory devices that operate solely on the spin orbit torque and UMR, which is critical for developing next-generation non volatile and low power consumption data storage technologies. △ Less

Submitted 17 May, 2024; originally announced May 2024.

Strain-dependent Insulating State and Kondo Effect in Epitaxial SrIrO$_{3}$ Films

Authors: Gaurab Rimal, Tanzila Tasnim, Gabriel Calderon Ortiz, George E. Sterbinsky, Jinwoo Hwang, Ryan B. Comes

Abstract: The large spin-orbit coupling in iridium oxides plays a significant role in driving novel physical behaviors, including emergent phenomena in the films and heterostructures of perovskite and Ruddlesden-Popper iridates. In this work, we study the role of epitaxial strain on the electronic behavior of thin SrIrO$_3$ films. We find that compressive epitaxial strain leads to metallic transport behavio… ▽ More The large spin-orbit coupling in iridium oxides plays a significant role in driving novel physical behaviors, including emergent phenomena in the films and heterostructures of perovskite and Ruddlesden-Popper iridates. In this work, we study the role of epitaxial strain on the electronic behavior of thin SrIrO$_3$ films. We find that compressive epitaxial strain leads to metallic transport behavior, but a slight tensile strain shows gapped behavior. Temperature-dependent resistivity measurements are used to examine different behaviors in films as a function of strain. We find Kondo contributions to the resistivity, with stronger effects in films that are thinner and under less compressive epitaxial strain. These results show the potential to tune SrIrO$_3$ into Kondo insulating states and open possibilities for a quantum critical point that can be controlled with strain in epitaxial films. △ Less

Submitted 16 April, 2024; originally announced April 2024.

Comments: 13 pages, 4 figures

Journal ref: Phys. Rev. Materials 8, L071201 (2024)

Spin-Energy Entanglement of a Time-Focused Neutron

Authors: J. C. Leiner, S. J. Kuhn, S. McKay, J. K. Jochum, F. Li, A. A. M. Irfan, F. Funama, D. Mettus, L. Beddrich, C. Franz, J. Shen, S. R. Parnell, R. M. Dalgliesh, M. Loyd, N. Geerits, G. Ortiz, C. Pfleiderer, R. Pynn

Abstract: Intra-particle entanglement of individual particles such as neutrons could enable another class of scattering probes that are sensitive to entanglement in quantum systems and materials. In this work, we present experimental results demonstrating quantum contextuality as a result of entanglement between the spin and energy modes (i.e., degrees of freedom) of single neutrons in a beam using a pair o… ▽ More Intra-particle entanglement of individual particles such as neutrons could enable another class of scattering probes that are sensitive to entanglement in quantum systems and materials. In this work, we present experimental results demonstrating quantum contextuality as a result of entanglement between the spin and energy modes (i.e., degrees of freedom) of single neutrons in a beam using a pair of resonant radio-frequency neutron spin flippers in the MIEZE configuration (Modulated IntEnsity with Zero Effort). We verified the mode-entanglement by measuring a Clauser-Horne-Shimony-Holt (CHSH) contextuality witness $S$ defined in the spin and energy subsystems, observing a clear breach of the classical bound of $|S| \leq 2$, obtaining $S = 2.40 \pm 0.02$. These entangled beams could enable alternative approaches for directly probing dynamics and entanglement in quantum materials whose low-energy excitation scales match those of the incident entangled neutron. △ Less

Submitted 30 September, 2024; v1 submitted 11 April, 2024; originally announced April 2024.

Comments: 11 pages, 7 figures

Journal ref: Physical Review Applied 22, L031005 (2024)

Entangled-Beam Reflectometry and Goos-Hänchen Shift

Authors: Q. Le Thien, R. Pynn, G. Ortiz

Abstract: We introduce the technique of Entangled-Beam Reflectometry for extracting spatially correlated (magnetic or non-magnetic) information from material surfaces or thin films. Our amplitude- and phase-sensitive technique exploits the coherent nature of an incoming entangled probe beam, of matter or light waves, undergoing reflection from the surface. Such reflection encodes the surface spatial structu… ▽ More We introduce the technique of Entangled-Beam Reflectometry for extracting spatially correlated (magnetic or non-magnetic) information from material surfaces or thin films. Our amplitude- and phase-sensitive technique exploits the coherent nature of an incoming entangled probe beam, of matter or light waves, undergoing reflection from the surface. Such reflection encodes the surface spatial structure into the probe's geometric and phase-derived Goos-Hänchen shifts, which can then be measured to unveil the structure. We investigate the way these shifts depend on the wave packet widths, and illustrate our technique in the case of in-plane periodic (non-)magnetic structures by utilizing spin-path mode-entangled neutron beams. △ Less

Submitted 21 January, 2024; originally announced January 2024.

Comments: 12 pages, including Supplemental Material

Topological Orders Beyond Topological Quantum Field Theories

Authors: P. Vojta, G. Ortiz, Z. Nussinov

Abstract: Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and pr… ▽ More Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and present a rich class of models exhibiting topological orders with distance-dependent interactions between anyons. As we illustrate, in some instances, the gapped lowest-energy excitations are comprised of anyons that densely cover the entire system. This leads to behaviors not typically described by topological quantum field theories. We examine these models by performing exact dualities to systems displaying conventional (i.e., Landau) orders. Our approach enables a general method for mapping generic Landau-type theories to dual models with topological order of the same spatial dimension. The low-energy subspaces of our models can be made more resilient to thermal effects than those of surface codes. △ Less

Submitted 14 August, 2024; v1 submitted 6 November, 2023; originally announced November 2023.

Comments: 15 pages, 4 figures

Emergent magnetic order in the antiferromagnetic Kitaev model with a [111] field

Authors: Will Holdhusen, Daniel Huerga, Gerardo Ortiz

Abstract: The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological $\mathbb{Z}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic field is a topic of current interest due to experiments, which apparently unveil a $\mathbb{Z}_2$ topological phase in the so-called Kitaev materials, and theoretic… ▽ More The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological $\mathbb{Z}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic field is a topic of current interest due to experiments, which apparently unveil a $\mathbb{Z}_2$ topological phase in the so-called Kitaev materials, and theoretical studies predicting the emergence of an intermediate quantum phase of debated nature before the appearance of a trivial partially polarized phase. In this work, we employ hierarchical mean-field theory, an algebraic and numerical method based on the use of clusters preserving relevant symmetries and short-range quantum correlations, to investigate the quantum phase diagram of the antiferromagnetic Kitaev's model in a [111] field. By using clusters of 24 sites, we predict that the Kitaev spin liquid transits through two intermediate phases characterized by stripe and chiral order, respectively, before entering the trivial partially polarized phase, differing from previous studies. We assess our results by performing exact diagonalization and computing the scaling of different observables, including the many-body Chern number and other topological quantities, thus establishing hierarchical mean-field theory as a method to study topological quantum spin liquids. △ Less

Submitted 6 November, 2023; originally announced November 2023.

Efficient homogenization of multicomponent metamaterials: chiral effects

Authors: W. Luis Mochán, Guillermo P. Ortiz

Abstract: We extend an efficient homogenization procedure based on a Haydock representation of the microscopic wave operator for the calculation of the macroscopic dielectric response of a periodic composite to the case of an arbitrary number of components of arbitrary composition. As a test, we apply our numerical procedure to the calculation of the optical properties of a Bouligand structure, made of a la… ▽ More We extend an efficient homogenization procedure based on a Haydock representation of the microscopic wave operator for the calculation of the macroscopic dielectric response of a periodic composite to the case of an arbitrary number of components of arbitrary composition. As a test, we apply our numerical procedure to the calculation of the optical properties of a Bouligand structure, made of a large number of anisotropic layers stacked on top of each other and progresively rotated. This system consitutes a photonic crystal with circularly polarized electromagnetic normal modes, naturally ocurring in the cuticle of several arthropods, and which has a gap for one polarization, which corresponds to the observation of circularly polarized strong metallic like reflections. Our numerical procedure is validated through its good agreement with the analytical solution for this simple chiral system. △ Less

Submitted 20 September, 2023; originally announced September 2023.

Comments: 25 pages, 7 figures, 30 refs

Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level

Authors: Arkadiusz Bochniak, Gerardo Ortiz

Abstract: Starting from Halperin multilayer systems we develop a hierarchical scheme that generates, bosonic and fermionic, single-layer quantum Hall states (or vacua) of arbitrary filling factor. Our scheme allows for the insertion of quasiparticle excitations with either Abelian or non-Abelian statistics and quantum numbers that depend on the nature of the original vacuum. Most importantly, it reveals a f… ▽ More Starting from Halperin multilayer systems we develop a hierarchical scheme that generates, bosonic and fermionic, single-layer quantum Hall states (or vacua) of arbitrary filling factor. Our scheme allows for the insertion of quasiparticle excitations with either Abelian or non-Abelian statistics and quantum numbers that depend on the nature of the original vacuum. Most importantly, it reveals a fusion mechanism for quasielectrons and magnetoexcitons that generalizes ideas about particle fractionalization introduced in A. Bochniak, Z. Nussinov, A. Seidel, and G. Ortiz, Commun. Phys. 5, 171 (2022) for the case of Laughlin fluids. In addition, in the second quantization representation, we uncover the inherent topological quantum order characterizing these vacua. In particular, we illustrate the methodology by constructing generalized composite (generalized Read) operators for the non-Abelian Pfaffian and Hafnian quantum fluid states. △ Less

Submitted 9 December, 2023; v1 submitted 7 August, 2023; originally announced August 2023.

Comments: 24 pages, 12 figures, final version

Journal ref: Phys. Rev. B 108, 245123 (2023)

Universal fragility of spin-glass ground-states under single bond changes

Authors: Mutian Shen, Gerardo Ortiz, Yang-Yu Liu, Martin Weigel, Zohar Nussinov

Abstract: We consider the effect of perturbing a single bond on ground-states of nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the coupling constants, across various two and three-dimensional lattices and regular random graphs. Our results reveal that the ground-states are strikingly susceptible to such changes. Altering the strength of only a single bond beyond a critical threshold v… ▽ More We consider the effect of perturbing a single bond on ground-states of nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the coupling constants, across various two and three-dimensional lattices and regular random graphs. Our results reveal that the ground-states are strikingly susceptible to such changes. Altering the strength of only a single bond beyond a critical threshold value leads to a new ground-state that differs from the original one by a droplet of flipped spins whose boundary and volume diverge with the system size -- an effect that is reminiscent of the more familiar phenomenon of disorder chaos. These elementary fractal-boundary zero-energy droplets and their composites feature robust characteristics and provide the lowest-energy macroscopic spin-glass excitations. Remarkably, within numerical accuracy, the size of such droplets conforms to a nearly universal power-law distribution with exponents dependent on the spatial dimension of the system. Furthermore, the critical coupling strengths adhere to a stretched Gaussian distribution that is predominantly determined by the local coordination number. △ Less

Submitted 14 March, 2024; v1 submitted 17 May, 2023; originally announced May 2023.

Comments: (14 pages, 8 figures)

Wiener-Hopf factorization approach to a bulk-boundary correspondence and stability conditions for topological zero-energy modes

Authors: Abhijeet Alase, Emilio Cobanera, Gerardo Ortiz, Lorenza Viola

Abstract: Both the physics and applications of fermionic symmetry-protected topological phases rely heavily on a principle known as bulk-boundary correspondence, which predicts the emergence of protected boundary-localized energy excitations (boundary states) if the bulk is topologically non-trivial. Current theoretical approaches formulate a bulk-boundary correspondence as an equality between a bulk and a… ▽ More Both the physics and applications of fermionic symmetry-protected topological phases rely heavily on a principle known as bulk-boundary correspondence, which predicts the emergence of protected boundary-localized energy excitations (boundary states) if the bulk is topologically non-trivial. Current theoretical approaches formulate a bulk-boundary correspondence as an equality between a bulk and a boundary topological invariant, where the latter is a property of boundary states. However, such an equality does not offer insight about the stability or the sensitivity of the boundary states to external perturbations. To solve this problem, we adopt a technique known as the Wiener-Hopf factorization of matrix functions. Using this technique, we first provide an elementary proof of the equality of the bulk and the boundary invariants for one-dimensional systems with arbitrary boundary conditions in all Altland-Zirnbauer symmetry classes. This equality also applies to quasi-one-dimensional systems (e.g., junctions) formed by bulks belonging to the same symmetry class. We then show that only topologically non-trivial Hamiltonians can host stable zero-energy edge modes, where stability refers to continuous deformation of zero-energy excitations with external perturbations that preserve the symmetries of the class. By leveraging the Wiener-Hopf factorization, we establish bounds on the sensitivity of such stable zero-energy modes to external perturbations. Our results show that the Wiener-Hopf factorization is a natural tool to investigate bulk-boundary correspondence in quasi-one-dimensional fermionic symmetry-protected topological phases. Our results on the stability and sensitivity of zero modes are especially valuable for applications, including Majorana-based topological quantum computing. △ Less

Submitted 7 April, 2023; originally announced April 2023.

Comments: 70 pages, 8 figures

Quasicriticality explains variability of human neural dynamics across life span

Authors: L. J. Fosque, A. Alipour, M. Zare, R. V. Williams-Garcia, J. M. Beggs, G. Ortiz

Abstract: Ageing impacts the brain's structural and functional organization and over time leads to various disorders, such as Alzheimer's disease and cognitive impairment. The process also impacts sensory function, bringing about a general slowing in various perceptual and cognitive functions. Here, we analyze the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) resting-state magnetoencephalography (M… ▽ More Ageing impacts the brain's structural and functional organization and over time leads to various disorders, such as Alzheimer's disease and cognitive impairment. The process also impacts sensory function, bringing about a general slowing in various perceptual and cognitive functions. Here, we analyze the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) resting-state magnetoencephalography (MEG) dataset -- the largest ageing cohort available -- in light of the quasicriticality framework, a novel organizing principle for brain functionality which relates information processing and scaling properties of brain activity to brain connectivity and stimulus. Examination of the data using this framework reveals interesting correlations with age and gender of test subjects. Using simulated data as verification, our results suggest a link between changes to brain connectivity due to ageing, and increased vulnerability to distraction from irrelevant information. Our findings suggest a platform to develop biomarkers of neurological health. △ Less

Submitted 6 September, 2022; originally announced September 2022.

Comments: 23 pages, 15 figures

A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions

Authors: Zohar Nussinov, Gerardo Ortiz

Abstract: We establish, in the spirit of the Lieb-Schultz-Mattis theorem, lower bounds on the spectral degeneracy of quantum systems with higher (Gauge Like) symmetries with rather generic physical boundary conditions in an arbitrary number of spatial dimensions. Contrary to applying twists or equivalent adiabatic operations, we exploit the effects of modified boundary conditions. When a general choice of b… ▽ More We establish, in the spirit of the Lieb-Schultz-Mattis theorem, lower bounds on the spectral degeneracy of quantum systems with higher (Gauge Like) symmetries with rather generic physical boundary conditions in an arbitrary number of spatial dimensions. Contrary to applying twists or equivalent adiabatic operations, we exploit the effects of modified boundary conditions. When a general choice of boundary geometry is immaterial in approaching the thermodynamic limit, systems that exhibit non-commuting Gauge Like symmetries, such as the orbital compass model, must have an exponential (in the size of the boundary) degeneracy of each of their spectral levels. We briefly discuss why, in spite of the proven large degeneracy associated with infrared-ultraviolet mixing, some systems may still exhibit conventional physical behaviors, i.e., of those of systems with non-extensive degeneracies, due to entropic "order by disorder" type effects. △ Less

Submitted 24 August, 2022; originally announced August 2022.

Comments: 21 pages, 3 figures

Quantum Quenches of an SO(5) Pseudospin Reveal Higgs Bosons

Authors: Qiao-Ru Xu, Gerardo Ortiz

Abstract: Controlled dynamical probe measurement of complex order parameter fluctuations may reveal its massive collective excitations. Here, we design dynamical quench protocols to excite independently all ten midgap Higgs bosons in the isotropic Balian--Werthamer state of a spinfull $p$-wave superfluid or superconductor. The analysis is based on microscopic equations of motion of an SO(5) pseudospin, an e… ▽ More Controlled dynamical probe measurement of complex order parameter fluctuations may reveal its massive collective excitations. Here, we design dynamical quench protocols to excite independently all ten midgap Higgs bosons in the isotropic Balian--Werthamer state of a spinfull $p$-wave superfluid or superconductor. The analysis is based on microscopic equations of motion of an SO(5) pseudospin, an extension of the usual Bloch equation to a five dimensional space. Key to these protocols is the realization of quenches that break the rotational symmetry of the kinetic energy and exploit the irreducible representation of the angular momentum $J=2$. For perturbative quenches, we find (non-decaying) periodic oscillations in time of these Higgs modes. Experiments to realize our proposal for either superfluids or superconductors are considered. △ Less

Submitted 25 March, 2023; v1 submitted 11 August, 2022; originally announced August 2022.

Comments: 6 pages, 3 figures

Journal ref: Phys. Rev. B 107, L100503 (2023)

Spin-Textured Neutron Beams with Orbital Angular Momentum

Authors: Quan Le Thien, Sam McKay, Roger Pynn, Gerardo Ortiz

Abstract: We present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterize… ▽ More We present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterized by a ``cork-screw'' phase singularity $e^{i \ell φ}$ about the propagation axis where $\ell$ is the OAM quantum number. To understand the precise relationship between the emergent OAM state and the variety of spin textures realized by various setups, we have developed a path-integral approach that in the interferometric limit makes a judicious use of magnetic Snell's law. We show that our proposed technique produces a complex two-dimensional pattern of spin-OAM entangled states which may be useful as a probe of quantum magnetic materials. We compare our path-integral approach to the well-known single-path Larmor precession model and present a pedagogical derivation of magnetic Snell's law of refraction for both massive and massless particles based on Maupertuis's action principle. △ Less

Submitted 6 April, 2023; v1 submitted 25 July, 2022; originally announced July 2022.

Comments: 23 pages, 7 figures, Physical Review B

Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

Authors: M. Tanhayi Ahari, S. Bandyopadhyay, Z. Nussinov, A. Seidel, G. Ortiz

Abstract: We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demons… ▽ More We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states. The emergent Entangled Pauli Principle (EPP), introduced in Phys. Rev. B 98, 161118(R) (2018) and which defines the ``DNA'' of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body $M$-clustering property within any given number of Landau levels. General arguments are supplemented by rigorous considerations for the $M=3$ case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement. △ Less

Submitted 7 April, 2023; v1 submitted 20 April, 2022; originally announced April 2022.

Comments: 52 pages, 18 figures, to appear in SciPost Physics

Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners

Authors: Laurens Lootens, Clement Delcamp, Gerardo Ortiz, Frank Verstraete

Abstract: We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by (non)-abelian groups but also more general categorical symmetries. These symmetries can be realized as matrix product operators which allow the extraction of a fusion category that c… ▽ More We present a systematic recipe for generating and classifying duality transformations in one-dimensional quantum lattice systems. Our construction emphasizes the role of global symmetries, including those described by (non)-abelian groups but also more general categorical symmetries. These symmetries can be realized as matrix product operators which allow the extraction of a fusion category that characterizes the algebra of all symmetric operators commuting with the symmetry. Known as the bond algebra, its explicit realizations are classified by module categories over the fusion category. A duality is then defined by a pair of distinct module categories giving rise to dual realizations of the bond algebra, as well as dual Hamiltonians. Symmetries of dual models are in general distinct but satisfy a categorical Morita equivalence. A key novelty of our categorical approach is the explicit construction of matrix product operators that intertwine dual bond algebra realizations at the level of the Hilbert space, and in general map local order operators to non-local string-order operators. We illustrate this approach for known dualities such as Kramers-Wannier, Jordan-Wigner, Kennedy-Tasaki and the IRF-vertex correspondence, a new duality of the $t$-$J_z$ chain model, and dualities in models with the exotic Haagerup symmetry. Finally, we comment on generalizations to higher dimensions. △ Less

Submitted 11 May, 2023; v1 submitted 16 December, 2021; originally announced December 2021.

Comments: 21 pages, v4: additional example, expanded discussion

Journal ref: PRX Quantum 4, 020357 (2023)

Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids

Authors: Arkadiusz Bochniak, Zohar Nussinov, Alexander Seidel, Gerardo Ortiz

Abstract: Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. Here we advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids, and uncover the fundamental… ▽ More Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. Here we advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids, and uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL). We show the first exact analytic computation of the quasielectron Berry connections leading to its fractional charge and exchange statistics, and perform Monte Carlo simulations that numerically confirm the fusion mechanism for quasiparticles. Thus, for instance, two quasiholes plus one electron of charge $e$ lead to an exact quasielectron of fractional charge $e/3$, and exchange statistics $1/3$, in a $ν=1/3$ Laughlin fluid. We express, in a compact manner, the sequence of (both bosonic and fermionic) Laughlin second-quantized states highlighting the lack of local condensation. Furthermore, we present a rigorous constructive subspace bosonization dictionary for the bulk fluid and establish universal long-distance behavior of edge excitations by formulating a conjecture based on the DNA, or root state, of the FQH fluid. △ Less

Submitted 18 April, 2022; v1 submitted 12 October, 2021; originally announced October 2021.

Comments: 17 pages, 4 figures

Journal ref: Communications Physics 5, 171 (2022)

Bloch and Bethe ansatze for the Harper model: A butterfly with a boundary

Authors: Qiao-Ru Xu, Emilio Cobanera, Gerardo Ortiz

Abstract: Based on a recent generalization of Bloch's theorem, we present a Bloch ansatz for the Harper model with an arbitrary rational magnetic flux in various geometries, and solve the associated ansatz equations analytically. In the case of a cylinder and a particular boundary condition, we find that the energy spectrum of edge states has no dependence on the length of the cylinder, which allows us to c… ▽ More Based on a recent generalization of Bloch's theorem, we present a Bloch ansatz for the Harper model with an arbitrary rational magnetic flux in various geometries, and solve the associated ansatz equations analytically. In the case of a cylinder and a particular boundary condition, we find that the energy spectrum of edge states has no dependence on the length of the cylinder, which allows us to construct a quasi-one-dimensional edge theory that is exact and describes two edges simultaneously. We prove that energies of bulk states, generating the so-called Hofstadter's butterfly, depend on a single geometry-dependent spectral parameter and have exactly the same functional form for the cylinder and the torus with general twisted boundary conditions, and argue that the (edge) bulk spectrum of a semi-infinite cylinder in an irrational magnetic field is (the complement of) a Cantor set. Finally, realizing that the bulk projection of the Harper Hamiltonian is a linear form over a deformed Weyl algebra, we introduce a Bethe ansatz valid for both cylinder and torus geometries. △ Less

Submitted 27 October, 2021; v1 submitted 21 July, 2021; originally announced July 2021.

Comments: 13+3 pages, 2+1 figures

Journal ref: Phys. Rev. B 104, 165140 (2021)

Integrable Model of Topological SO(5) Superfluidity

Authors: Will J. Holdhusen, Sergio Lerma-Hernández, Jorge Dukelsky, Gerardo Ortiz

Abstract: Assisted by general symmetry arguments and a many-body invariant, we introduce a phase of matter that constitutes a topological SO(5) superfluid. Key to this finding is the realization of an exactly solvable model that displays some similarities with a minimal model of superfluid $^3$He. We study its quantum phase diagram and correlations, and find exotic superfluid as well as metallic phases in t… ▽ More Assisted by general symmetry arguments and a many-body invariant, we introduce a phase of matter that constitutes a topological SO(5) superfluid. Key to this finding is the realization of an exactly solvable model that displays some similarities with a minimal model of superfluid $^3$He. We study its quantum phase diagram and correlations, and find exotic superfluid as well as metallic phases in the repulsive sector. At the critical point separating trivial and nontrivial superfluid phases, our Hamiltonian reduces to the globally SO(5)-symmetric Gaudin model with a degenerate ground manifold that includes quartet states. Most importantly, the exact solution permits uncovering of an interesting non-pair-breaking mechanism for superfluids subject to external magnetic fields. Nonintegrable modifications of our model lead to a strong-coupling limit of our metallic phase with a ground-state manifold that shows an extensive entropy. △ Less

Submitted 21 September, 2021; v1 submitted 31 January, 2021; originally announced February 2021.

Journal ref: Phys. Rev. B 104, 060503 (2021)

Neutron State Entanglement with Overlapping Paths

Authors: S. J. Kuhn, S. McKay, J. Shen, N. Geerits, R. M. Dalgliesh, E. Dees, A. A. M. Irfan, F. Li, S. Lu, V. Vangelista, D. V. Baxter, G. Ortiz, S. R. Parnell, W. M. Snow, R. Pynn

Abstract: The development of direct probes of entanglement is integral to the rapidly expanding field of complex quantum materials. Here we test the robustness of entangled neutrons as a quantum probe by measuring the Clauser-Horne-Shimony-Holt contextuality witness while varying the beam properties. Specifically, we prove that the entanglement of the spin and path subsystems of individual neutrons prepared… ▽ More The development of direct probes of entanglement is integral to the rapidly expanding field of complex quantum materials. Here we test the robustness of entangled neutrons as a quantum probe by measuring the Clauser-Horne-Shimony-Holt contextuality witness while varying the beam properties. Specifically, we prove that the entanglement of the spin and path subsystems of individual neutrons prepared in two different experiments using two different apparatuses persists even after varying the entanglement length, coherence length, and neutron energy difference of the paths. The two independent apparatuses acting as entangler-disentangler pairs are static-field magnetic Wollaston prisms and resonance-field radio frequency flippers. Our results show that the spatial and energy properties of the neutron beam may be significantly altered without reducing the contextuality witness value below the Tsirelson bound, meaning that maximum entanglement is preserved. We also show that two paths may be considered distinguishable even when separated by less than the neutron coherence length. This work is the key step in the realization of the new modular, robust technique of entangled neutron scattering. △ Less

Submitted 21 December, 2020; originally announced December 2020.

Journal ref: Phys. Rev. Research 3, 023227 (2021)

Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology

Authors: Abhishek Kumar, Gerardo Ortiz, Philip Richerme, Babak Seradjeh

Abstract: We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high-frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY an… ▽ More We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high-frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interaction (DMI) terms. The dynamically generated magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. As these phases are cycled, the current reveals the ground-state degeneracies that distinguish the ordered and disordered phases. We discuss experimental requirements needed to realize the Floquet gauge pump in a synthetic quantum spin system of interacting trapped ions. △ Less

Submitted 21 May, 2021; v1 submitted 17 December, 2020; originally announced December 2020.

Comments: 4.5 pages, 4 figures + supplemental material

Journal ref: Phys. Rev. Lett. 126, 206602 (2021)

Evidence for quasicritical brain dynamics

Authors: Leandro Fosque, Rashid V. Williams-Garcia, John M. Beggs, Gerardo Ortiz

Abstract: Much evidence seems to suggest cortex operates near a critical point, yet a single set of exponents defining its universality class has not been found. In fact, when critical exponents are estimated from data, they widely differ across species, individuals of the same species, and even over time, or depending on stimulus. Interestingly, these exponents still approximately hold to a dynamical scali… ▽ More Much evidence seems to suggest cortex operates near a critical point, yet a single set of exponents defining its universality class has not been found. In fact, when critical exponents are estimated from data, they widely differ across species, individuals of the same species, and even over time, or depending on stimulus. Interestingly, these exponents still approximately hold to a dynamical scaling relation. Here we show that the theory of quasicriticality, an organizing principle for brain dynamics, can account for this paradoxical situation. As external stimuli drive the cortex, quasicriticality predicts a departure from criticality along a Widom line with exponents that decrease in absolute value, while still holding approximately to a dynamical scaling relation. We use simulations and experimental data to confirm these predictions and describe new ones that could be tested soon. △ Less

Submitted 7 May, 2021; v1 submitted 6 October, 2020; originally announced October 2020.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 126, 098101 (2021)

Quantum Entangled-Probe Scattering Theory

Authors: Abu Ashik Md Irfan, Patrick Blackstone, Roger Pynn, Gerardo Ortiz

Abstract: We develop an entangled-probe scattering theory, including quantum detection, that extends the scope of standard scattering approaches. We argue that these probes may be revolutionary in studying entangled matter such as unconventional phases of strongly correlated systems. Our presentation focuses on a neutron beam probe that is mode-entangled in spin and path as is experimentally realized in [1]… ▽ More We develop an entangled-probe scattering theory, including quantum detection, that extends the scope of standard scattering approaches. We argue that these probes may be revolutionary in studying entangled matter such as unconventional phases of strongly correlated systems. Our presentation focuses on a neutron beam probe that is mode-entangled in spin and path as is experimentally realized in [1], although similar ideas also apply to photon probes. We generalize the traditional van Hove theory [2] whereby the response is written as a properly-crafted combination of two-point correlation functions. Tuning the probe's entanglement length allows us to interrogate spatial scales of interest by analyzing interference patterns in the differential cross-section. Remarkably, for a spin dimer target we find that the typical Young-like interference pattern observed if the target state is un-entangled gets quantum erased when that state becomes maximally entangled. △ Less

Submitted 11 July, 2021; v1 submitted 10 August, 2020; originally announced August 2020.

Comments: 13 pages, 8 figures. Published in New Journal of Physics

Squaring the fermion: The threefold way and the fate of zero modes

Authors: Qiao-Ru Xu, Vincent P. Flynn, Abhijeet Alase, Emilio Cobanera, Lorenza Viola, Gerardo Ortiz

Abstract: We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary spa… ▽ More We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension we establish three fundamental no-go theorems that prove the absence of: parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting non-interacting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of non-interacting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models. △ Less

Submitted 24 June, 2020; v1 submitted 12 May, 2020; originally announced May 2020.

Comments: 26+5 pages, 3 figures, 9 tables

Journal ref: Phys. Rev. B 102, 125127 (2020)

Stable Calculation of Optical Properties of Large Non-Periodic Dissipative Multilayered Systems

Authors: Luis Eduardo Puente-Díaz, Victor Castillo-Gallardo, Guillermo P. Ortiz, José Samuel Pérez-Huerta, Héctor Pérez-Aguilar, Vivechana Agarwal, W. Luis Mochán

Abstract: The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total matrix to solve for all the fields at all the interfaces simultaneously and an expansion in the Bloch-like modes of a periodic artificially repeated system. We a… ▽ More The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total matrix to solve for all the fields at all the interfaces simultaneously and an expansion in the Bloch-like modes of a periodic artificially repeated system. We apply both methods to obtain the reflectance spectra of multilayered chirped structures composed of nanostructured porous silicon (PS). Both methods yield reliable and numerically stable results. The former allows an analysis of the field within all layers while the latter is much more efficient computationally, allowing the design of novel structures and the optimization of their parameters. We compare numerical and experimental results across a wide spectral range from the infrared to the ultraviolet. △ Less

Submitted 2 May, 2020; originally announced May 2020.

Comments: 20 pages, 7 figures

An Operator Analysis of Contextuality Witness Measurements for Multimode-Entangled Single Neutron Interferometry

Authors: Shufan Lu, Abu Ashik Md. Irfan, Jiazhou Shen, Steve J. Kuhn, W. Michael Snow, David V. Baxter, Roger Pynn, Gerardo Ortiz

Abstract: We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describ… ▽ More We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutron state space is approximated by a finite tensor product of distinguishable subsystems. We design entangled-neutron interferometers to measure entanglement witnesses for the Clauser, Horne, Shimony and Holt, and Mermin inequalities, and compare the theoretical predictions with recent experimental results. We present the generalization of these expressions to $n$ entangled distinguishable subsystems, which could become relevant in the future if it becomes possible to add neutron orbital angular momentum to the experimentally-accessible list of entangled modes. We view this work as a necessary first step towards a theoretical description of entangled neutron scattering from strongly entangled matter, and we explain why it should be possible to formulate a useful generalization of the usual Van Hove linear response theory for this case. We also briefly describe some other scientific extensions and applications which can benefit from interferometric measurements using the types of single-neutron multimode entanglement described by this analysis. △ Less

Submitted 21 December, 2019; originally announced December 2019.

Comments: 18 pages, 11 figures

Journal ref: Phys. Rev. A 101, 042318 (2020)

Local two-body parent Hamiltonians for the entire Jain sequence

Authors: Sumanta Bandyopadhyay, Gerardo Ortiz, Zohar Nussinov, Alexander Seidel

Abstract: Using an algebra of second quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor $n/(2n{\sf p}+1)$, with integer $n$, and (half-)integer ${\sf p}$. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish an… ▽ More Using an algebra of second quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor $n/(2n{\sf p}+1)$, with integer $n$, and (half-)integer ${\sf p}$. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish an associated "entangled Pauli principle" describing these states and associated zero mode spaces, as well as an emergent SU($n$) symmetry. △ Less

Submitted 20 May, 2020; v1 submitted 17 October, 2019; originally announced October 2019.

Comments: 14 pages, 2 figures, published version, extended and improved supplement

Journal ref: Phys. Rev. Lett. 124, 196803 (2020)

Recursive Calculation of the Optical Response of Multicomponent Metamaterials

Authors: W. Luis Mochán, Raksha Singla, Lucila Juárez, Guillermo P. Ortiz

Abstract: We develop a recursive computational procedure to efficiently calculate the macroscopic dielectric function of multi-component metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the microscopic response of the system might correspond to non-Hermitian operators, we develop a representation of the microscopic fields and of the response, and we intr… ▽ More We develop a recursive computational procedure to efficiently calculate the macroscopic dielectric function of multi-component metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the microscopic response of the system might correspond to non-Hermitian operators, we develop a representation of the microscopic fields and of the response, and we introduce an appropriate metric that makes all operators symmetric. This allows us to use a modified Haydock recursion, introducing complex Haydock coefficients that allow an efficient computation of the macroscopic response and the microscopic fields. We test our procedure comparing our results to analytical ones in simple systems, and verifying they obey a generalized multicomponent Keller's theorem and the Mortola and Stefé's theorem for four component metalic and dielectric systems. △ Less

Submitted 20 September, 2019; originally announced September 2019.

Comments: 10 pages, 4 figures. Phys. Status Solidi B (2020)

Journal ref: Physica Status Solidi B: Basic Solid State Physics 257, 1900560 (2020)

Unveiling contextual realities by microscopically entangling a neutron

Authors: J. Shen, S. J. Kuhn, R. M. Dalgliesh, V. O. de Haan, N. Geerits, A. A. M. Irfan, F. Li, S. Lu, S. R. Parnell, J. Plomp, A. A. van Well, A. Washington, D. V. Baxter, G. Ortiz, W. M. Snow, R. Pynn

Abstract: The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. The dramatic progress made by modern probe techniques to uncover the microscopic structure of matter is fundamentally rooted in our control of two defining traits of quantum mechanics: discreteness of physical properties and interference phenomena. Magnetic Reso… ▽ More The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. The dramatic progress made by modern probe techniques to uncover the microscopic structure of matter is fundamentally rooted in our control of two defining traits of quantum mechanics: discreteness of physical properties and interference phenomena. Magnetic Resonance Imaging, for instance, exploits the fact that protons have spin and can absorb photons at frequencies that depend on the medium to image the anatomy and physiology of living systems. Scattering techniques, in which photons, electrons, protons or neutrons are used as probes, make use of quantum interference to directly image the spatial position of individual atoms, their magnetic structure, or even unveil their concomitant dynamical correlations. None of these probes have so far exploited a unique characteristic of the quantum world: entanglement. Here we introduce a fundamentally new quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. Its tunable entanglement length from nanometers to microns and energy differences from peV to neV will enable new investigations of microscopic magnetic correlations in systems with strongly entangled phases, such as those believed to emerge in unconventional superconductors. We develop an interferometer to prove entanglement of these distinguishable properties of the neutron beam by observing clear violations of both Clauser-Horne-Shimony-Holt and Mermin contextuality inequalities in the same experimental setup. Our work opens a pathway to a future era of entangled neutron scattering in matter. △ Less

Submitted 26 August, 2019; originally announced August 2019.

Comments: 11 pages, 4 figures

Integrable model of a $p$-wave bosonic superfluid

Authors: Sergio Lerma-Hernandez, Jorge Dukelsky, Gerardo Ortiz

Abstract: We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair… ▽ More We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state. △ Less

Submitted 9 November, 2019; v1 submitted 7 August, 2019; originally announced August 2019.

Comments: Phys. Rev. Res. (RC)

Journal ref: Phys. Rev. Research 1, 032021 (2019)

Phase transitions in the $\mathbb{Z}_p$ and U(1) clock models

Authors: G. Sun, T. Vekua, E. Cobanera, G. Ortiz

Abstract: Quantum phase transitions are studied in the non-chiral $p$-clock chain, and a new explicitly U(1)-symmetric clock model, by monitoring the ground-state fidelity susceptibility. For $p\ge 5$, the self-dual $\mathbb{Z}_p$-symmetric chain displays a double-hump structure in the fidelity susceptibility with both peak positions and heights scaling logarithmically to their corresponding thermodynamic v… ▽ More Quantum phase transitions are studied in the non-chiral $p$-clock chain, and a new explicitly U(1)-symmetric clock model, by monitoring the ground-state fidelity susceptibility. For $p\ge 5$, the self-dual $\mathbb{Z}_p$-symmetric chain displays a double-hump structure in the fidelity susceptibility with both peak positions and heights scaling logarithmically to their corresponding thermodynamic values. This scaling is precisely as expected for two Beresinskii-Kosterlitz-Thouless (BKT) transitions located symmetrically about the self-dual point, and so confirms numerically the theoretical scenario that sets $p=5$ as the lowest $p$ supporting BKT transitions in $\mathbb{Z}_p$-symmetric clock models. For our U(1)-symmetric, non-self-dual minimal modification of the $p$-clock model we find that the phase diagram depends strongly on the parity of $p$ and only one BKT transition survives for $p\geq 5$. Using asymptotic calculus we map the self-dual clock model exactly, in the large $p$ limit, to the quantum $O(2)$ rotor chain. Finally, using bond-algebraic dualities we estimate the critical BKT transition temperatures of the classical planar $p$-clock models defined on square lattices, in the limit of extreme spatial anisotropy. Our values agree remarkably well with those determined via classical Monte Carlo for isotropic lattices. This work highlights the power of the fidelity susceptibility as a tool for diagnosing the BKT transitions even when only discrete symmetries are present. △ Less

Submitted 19 September, 2019; v1 submitted 21 July, 2019; originally announced July 2019.

Comments: 17 pages, 14 figures

Journal ref: Phys. Rev. B 100, 094428 (2019)

Universality Classes of Stabilizer Code Hamiltonians

Authors: Zack Weinstein, Gerardo Ortiz, Zohar Nussinov

Abstract: Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to generically solve their partition function using duality techniques. By unveiling each model's universality class and effective dimension, insights may be gained… ▽ More Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to generically solve their partition function using duality techniques. By unveiling each model's universality class and effective dimension, insights may be gained on their finite temperature dynamics and robustness. Our technique is demonstrated in particular on the 4D Toric Code and Haah's Code -- we find that the former falls into the 4D Ising universality class, whereas Haah's Code exhibits dimensional reduction and falls into the 1D Ising universality class. △ Less

Submitted 27 November, 2019; v1 submitted 9 July, 2019; originally announced July 2019.

Comments: 10 pages, 2 figures, 1 table; v2: added references, fixed minor typos

Journal ref: Phys. Rev. Lett. 123, 230503 (2019)

Certified Quantum Measurement of Majorana Fermions

Authors: Abu Ashik Md. Irfan, Karl Mayer, Gerardo Ortiz, Emanuel Knill

Abstract: We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of… ▽ More We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\langle W \rangle \le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\langle W \rangle=5$ indicates the degree of confidence in the detection of Majorana fermions. △ Less

Submitted 27 April, 2019; originally announced April 2019.

Comments: 13 pages, 3 figures

Journal ref: Phys. Rev. A 101, 032106 (2020)

Absence of Finite Temperature Phase Transitions in the X-Cube Model and its $\mathbb{Z}_{p}$ Generalization

Authors: Zack Weinstein, Emilio Cobanera, Gerardo Ortiz, Zohar Nussinov

Abstract: We investigate thermal properties of the X-Cube model and its $\mathbb{Z}_{p}$ `clock-type' ($p$X-Cube) extension. In the latter, the elementary spin-1/2 operators of the X-Cube model are replaced by elements of the Weyl algebra. We study different boundary condition realizations of these models and analyze their finite temperature dynamics and thermodynamics. We find that (i) no finite temperatur… ▽ More We investigate thermal properties of the X-Cube model and its $\mathbb{Z}_{p}$ `clock-type' ($p$X-Cube) extension. In the latter, the elementary spin-1/2 operators of the X-Cube model are replaced by elements of the Weyl algebra. We study different boundary condition realizations of these models and analyze their finite temperature dynamics and thermodynamics. We find that (i) no finite temperature phase transitions occur in these systems. In tandem, employing bond-algebraic dualities, we show that for Glauber type solvable baths, (ii) thermal fluctuations might not enable system size dependent time autocorrelations at all positive temperatures (i.e., they are thermally fragile). Qualitatively, our results demonstrate that similar to Kitaev's Toric code model, the X-Cube model (and its $p$-state clock-type descendants) may be mapped to simple classical Ising ($p$-state clock) chains in which neither phase transitions nor anomalously slow glassy dynamics might appear. △ Less

Submitted 27 November, 2019; v1 submitted 11 December, 2018; originally announced December 2018.

Comments: 67 pages, 18 figures; v4: minor typos corrected

Journal ref: Ann. Phys. 412, 168018 (2020)

Generalization of Bloch's theorem for arbitrary boundary conditions: Interfaces and topological surface band structure

Authors: Emilio Cobanera, Abhijeet Alase, Gerardo Ortiz, Lorenza Viola

Abstract: We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. Our method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schro… ▽ More We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. Our method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrodinger equation is compatible with a partial Fourier transform operation. Bulk equations may display unusual features because they are relative eigenvalue problems for non-Hermitian, bulk-projected Hamiltonians. Nonetheless, they admit a rich symmetry analysis that can simplify considerably the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our extension of the generalized Bloch theorem to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulator hosting topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral $p+ip$ two-dimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless $s$-wave topological superconductor. We analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the $4π$-periodic supercurrent. △ Less

Submitted 22 August, 2018; originally announced August 2018.

Comments: 20+9 pages, 10 figures

Journal ref: Phys. Rev. B 98, 245423 (2018)

Entangled Pauli Principles: the DNA of Quantum Hall Fluids

Authors: Sumanta Bandyopadhyay, Li Chen, Mostafa Tanhayi Ahari, Gerardo Ortiz, Zohar Nussinov, Alexander Seidel

Abstract: A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through "generalized Pauli principles" is expanded to allow for root level entanglement, giving rise to "entangled Pauli principles". Through the latter, aspects of the effective field theory description become ingrained in exact microscopic sol… ▽ More A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through "generalized Pauli principles" is expanded to allow for root level entanglement, giving rise to "entangled Pauli principles". Through the latter, aspects of the effective field theory description become ingrained in exact microscopic solutions for a great wealth of phases for which no similar single Landau level description is known. We discuss in detail braiding statistic, edge theory, and rigorous zero mode counting for the Jain-221 state as derived from a microscopic Hamiltonian. The relevant root-level entanglement is found to feature an AKLT-type MPS structure associated with an emergent SU(2) symmetry. △ Less

Submitted 19 March, 2018; v1 submitted 2 March, 2018; originally announced March 2018.

Comments: 12 pages, including supplemental. Revised version includes two references corresponding to multi-layer graphene

Journal ref: Phys. Rev. B 98, 161118 (2018)

The Binomial Spin Glass

Authors: Mohammad-Sadegh Vaezi, Gerardo Ortiz, Martin Weigel, Zohar Nussinov

Abstract: To establish a unified framework for studying both discrete and continuous coupling distributions, we introduce the {\it binomial} spin glass, a class of models where the couplings are sums of $m$ identically distributed Bernoulli random variables. In the continuum limit $m \to \infty$, the class reduces to one with Gaussian couplings, while $m=1$ corresponds to the $\pm J$ spin glass. We demonstr… ▽ More To establish a unified framework for studying both discrete and continuous coupling distributions, we introduce the {\it binomial} spin glass, a class of models where the couplings are sums of $m$ identically distributed Bernoulli random variables. In the continuum limit $m \to \infty$, the class reduces to one with Gaussian couplings, while $m=1$ corresponds to the $\pm J$ spin glass. We demonstrate that for short-range Ising models on $d$-dimensional hypercubic lattices the ground-state entropy density for $N$ spins is bounded from above by $(\sqrt{d/2m} + 1/N)\ln2$, and further show that the actual entropies follow the scaling behavior implied by this bound. We thus uncover a fundamental non-commutativity of the thermodynamic and continuous coupling limits that leads to the presence or absence of degeneracies depending on the precise way the limits are taken. Exact calculations of defect energies reveal a crossover length scale $L^\ast(m) \sim L^κ$ below which the binomial spin glass is indistinguishable from the Gaussian system. Since $κ= -1/(2θ)$, where $θ$ is the spin-stiffness exponent, discrete couplings become irrelevant at large scales for systems with a finite-temperature spin-glass phase. △ Less

Submitted 22 July, 2018; v1 submitted 22 December, 2017; originally announced December 2017.

Journal ref: Phys. Rev. Lett. 121, 080601 (2018)

Topological superfluidity with repulsive alkaline-earth atoms in optical lattices

Authors: L. Isaev, A. Kaufman, G. Ortiz, A. M. Rey

Abstract: Topological superfluids are of technological relevance since they are believed to host Majorana bound states, a powerful resource for quantum computation and memory. Here we propose to realize topological superfluidity with fermionic atoms in an optical lattice. We consider a situation where atoms in two internal states experience different lattice potentials: one species is localized and the othe… ▽ More Topological superfluids are of technological relevance since they are believed to host Majorana bound states, a powerful resource for quantum computation and memory. Here we propose to realize topological superfluidity with fermionic atoms in an optical lattice. We consider a situation where atoms in two internal states experience different lattice potentials: one species is localized and the other itinerant, and show how quantum fluctuations of the localized fermions give rise to an attraction and strong spin-orbit coupling in the itinerant band. At low temperature, these effects stabilize a topological superfluid of mobile atoms even if their bare interactions are repulsive. This emergent state can be engineered with ${}^{87}$Sr atoms in a superlattice with a dimerized unit cell. To probe its unique properties we describe protocols that use high spectral resolution and controllability of the Sr clock transition, such as momentum-resolved spectroscopy and supercurrent response to a synthetic (laser-induced) magnetic field. △ Less

Submitted 7 October, 2017; originally announced October 2017.

A generalization of Bloch's theorem for arbitrary boundary conditions: Theory

Authors: Abhijeet Alase, Emilio Cobanera, Gerardo Ortiz, Lorenza Viola

Abstract: We present a generalization of Bloch's theorem to finite-range lattice systems of independent fermions, in which translation symmetry is broken only by arbitrary boundary conditions, by providing exact, analytic expressions for all energy eigenvalues and eigenstates. By transforming the single-particle Hamiltonian into a corner-modified banded block-Toeplitz matrix, a key step is a bipartition of… ▽ More We present a generalization of Bloch's theorem to finite-range lattice systems of independent fermions, in which translation symmetry is broken only by arbitrary boundary conditions, by providing exact, analytic expressions for all energy eigenvalues and eigenstates. By transforming the single-particle Hamiltonian into a corner-modified banded block-Toeplitz matrix, a key step is a bipartition of the lattice, which splits the eigenvalue problem into a system of bulk and boundary equations. The eigensystem inherits most of its solutions from an auxiliary, infinite translation-invariant Hamiltonian that allows for non-unitary representations of translation symmetry. A reformulation of the boundary equation in terms of a boundary matrix ensures compatibility with the boundary conditions, and determines the allowed energy eigenstates. We show how the boundary matrix captures the interplay between bulk and boundary properties, leading to efficient indicators of bulk-boundary correspondence. Remarkable consequences of our generalized Bloch theorem are the engineering of Hamiltonians that host perfectly localized, robust zero-energy edge modes, and the predicted emergence, e.g. in Kitaev's chain, of localized excitations whose amplitudes decay exponentially with a power-law prefactor. We further show how the theorem yields diagonalization algorithms for the class of Hamiltonians under consideration, and use the proposed bulk-boundary indicator to characterize the topological response of a multi-band time-reversal invariant s-wave superconductor under twisted boundary conditions, showing how a fractional Josephson effect can occur without a fermionic parity switch. Finally, we establish connections to the transfer matrix method and demonstrate, using the paradigmatic Kitaev's chain example, that a non-diagonalizable transfer matrix signals the presence of solutions with a power-law prefactor. △ Less

Submitted 27 June, 2017; originally announced June 2017.

Comments: 34 pages (including appendices), 8 color figures

Journal ref: Phys. Rev. B 96, 195133 (2017)