Showing 1–39 of 39 results for author: Green, D

Nonplanar qubit with tunable gauge symmetry

Authors: Muqing Yu, Han Bi, Hengli Lo, Vishvesha Sridhar, Guilherme Delfino, Dmitry Green, Claudio Chamon, Nadya Mason, Andrew P. Higginbotham

Abstract: Circuit quantum electrodynamics embeds Josephson junction qubits within superconducting cavities, and has emerged as a leading approach to quantum computing and quantum simulation. Despite the many permutations of circuit geometry that have been explored, Josephson connectivities have so far been planar, making them effectively low-dimensional. Here we show that a non-planar qubit -- a $3\times3$… ▽ More Circuit quantum electrodynamics embeds Josephson junction qubits within superconducting cavities, and has emerged as a leading approach to quantum computing and quantum simulation. Despite the many permutations of circuit geometry that have been explored, Josephson connectivities have so far been planar, making them effectively low-dimensional. Here we show that a non-planar qubit -- a $3\times3$ crossbar Josephson array -- gives rise to flux-tunable $\mathbb{Z}_3$ combinatorial gauge symmetry (CGS), potentially enabling spin-liquid behavior when networked into a lattice. The observed excitation spectrum shows excellent agreement with predictions from a neural network trained to generate variational quantum states, demonstrating that we have predictive power over our high-dimensional quantum system. Fine-structure splittings near the CGS point are compatible with weak tunneling or symmetry breaking due to experimental imperfections. We additionally use the superconducting cavity to externally induce symmetry breaking, observing a restoration of symmetry at the CGS point where ground states differ only by a $\mathbb{Z}_3$ phase. This work initiates a general program exploring lattice gauge theories using the toolbox of circuit quantum electrodynamics. More broadly, introducing non-planar Josephson connectivities opens a vast space for experimental and theoretical exploration of structures in almost any imaginable dimensionality and geometry. △ Less

Submitted 15 July, 2026; originally announced July 2026.

Comments: 7+14 pages, 5+7 figures

A Computational Study of Organic Molecular Crystals for Photocatalytic Water Splitting

Authors: James D. Green, Daniel G. Medranda, Hong Wang, Andrew I. Cooper, Jenny Nelson, Kim E. Jelfs

Abstract: Organic crystalline materials are potential candidates for photocatalytic overall water splitting (OWS). Although organic crystals have been heavily investigated for application in organic electronics, such as organic light-emitting diodes (OLEDs) and solar cells, there have been comparatively fewer studies into OWS in these materials. A major challenge is the large number of electronic and struct… ▽ More Organic crystalline materials are potential candidates for photocatalytic overall water splitting (OWS). Although organic crystals have been heavily investigated for application in organic electronics, such as organic light-emitting diodes (OLEDs) and solar cells, there have been comparatively fewer studies into OWS in these materials. A major challenge is the large number of electronic and structural criteria that must be met for a material to make a viable OWS photocatalyst. Optical absorption, reduction and oxidation potentials and charge-transport properties are among the key considerations, and these are influenced both by molecular properties and the solid-state packing arrangement, making computational modelling challenging. Here, we investigate a series of known organic electronic materials that have published crystal structures using periodic density functional theory (DFT) and compare their calculated electronic properties of optical absorption and reduction and oxidation potentials with literature experimental data. Furthermore we perform a series of gas-phase molecular calculations which show a good agreement with literature data and periodic DFT for the optoelectronic properties of the organic molecular crystals studied, showing that gas-phase molecular calculations could be used to screen organic crystals for OWS at a reduced computational cost. △ Less

Submitted 20 February, 2026; originally announced February 2026.

Coulombic control of charge transfer in luminescent radicals with long-lived quartet states

Authors: Lujo Matasovic, Petri Murto, Shilong Yu, Wenzhao Wang, James D. Green, Giacomo Londi, Weixuan Zeng, Laura Brown, William K. Myers, David Beljonne, Yoann Olivier, Feng Li, Hugo Bronstein, Timothy J. H. Hele, Richard H. Friend, Sebastian Gorgon

Abstract: Excitons in organic materials are emerging as an attractive platform for tunable quantum technologies. Structures with near-degenerate doublet and triplet excitations in linked trityl radical, acene and carbazole units can host quartet states. These high spin states can be coherently manipulated, and later decay radiatively via the radical doublet transition. However, this requires controlling the… ▽ More Excitons in organic materials are emerging as an attractive platform for tunable quantum technologies. Structures with near-degenerate doublet and triplet excitations in linked trityl radical, acene and carbazole units can host quartet states. These high spin states can be coherently manipulated, and later decay radiatively via the radical doublet transition. However, this requires controlling the deexcitation pathways of all metastable states. Here we establish design rules for efficient quartet generation in luminescent radicals, using different connection arrangements of the molecular units. We discover that electronic coupling strength between these units dictates luminescence and quartet formation yields, particularly through the energetics of an acene-radical charge transfer state, which we tune Coulombically. This state acts as a source of non-radiative decay when acene-radical separation is small, but facilitates doublet-quartet spin interconversion when acene-radical separation is large. Using these rules we report a radical-carbazole-acene material with 55% luminescence yield, where 94% of emitting excitons originate from the quartet at microsecond times. This reveals the central role of molecular topology in luminescent quantum materials. △ Less

Submitted 9 August, 2025; originally announced August 2025.

Comments: 22 pages, 4 figures

Design and demonstration of a direct air capture system with moisture-driven CO2 delivery into aqueous medium

Authors: Justin Flory, Samantha Taylor, Shuqin Li, Sunil Tiwari, Garrett Cole, Amory Lowe, Lindsey Hamblin, Samuel Piorkowski, Matthew Ryan, Thiago Stangherlin Barbosa, Jason Kmon, Nick Lowery, Joel Eliston, Jason C. Quinn, John McGowen, Matthew D. Green, Klaus Lackner, Wim Vermaas

Abstract: A moisture-driven air capture (DAC) system was designed and demonstrated. A laboratory-scale system delivering ~1 g CO2 per day was demonstrated in a laminar flow hood and a small pilot-scale system that could deliver ~100 g CO2 daily was operated outdoors in a 4.2 m2 (areal surface area) raceway pond. Elongated mesh tube packets were designed to contain AER beads with high surface area for contac… ▽ More A moisture-driven air capture (DAC) system was designed and demonstrated. A laboratory-scale system delivering ~1 g CO2 per day was demonstrated in a laminar flow hood and a small pilot-scale system that could deliver ~100 g CO2 daily was operated outdoors in a 4.2 m2 (areal surface area) raceway pond. Elongated mesh tube packets were designed to contain AER beads with high surface area for contacting the air and were found to reduce drying and CO2 loading time ~4-fold over larger mesh bags. Whereas this system was designed for CO2 delivery for cultivating photosynthetic microbes, its potential uses are much broader and include CO2 use in the food and beverage industry, conversion to fuels and chemicals, and sequestration. Techno-economic assessments for a practical scenario based on current results are \$670/tonne to capture CO2 into an alkaline solution and an additional \$280/tonne to extract CO2 from solution, purify and compress to 15 MPa for sequestration. An aspirational scenario modelling reasonable improvements to develop AER sorbents with a capacity of 4 mmol CO2 per gram of sorbent and water uptake of 50 wt.%, which leads to sorbent drying and loading within 1 h, shows a potential to reach \$51/tonne to capture CO2 into an alkaline solution and an additional \$109/tonne to get to 15 MPa for sequestration. Life cycle analysis shows the aspirational moisture-driven process uses up to 87% less energy than thermal and/or vacuum swing DAC by using energy from water evaporation; however, ~330 wt.% water uptake by the sorbent contained in a hydrophilic mesh packets leads to ~33-fold higher water use than the thermodynamic limits, which emphasizes future research is needed to increase sorbent hydrophobicity while maintaining and further increasing ion exchange capacity needed to bind CO2. △ Less

Submitted 4 August, 2025; originally announced August 2025.

Comments: 14 pages, 11 figures. To be submitted to Energy & Environmental Science

Characterizing and modeling the mechanical behavior of an anion exchange membrane for carbon capture applications

Authors: Sara Sarbaz, Zhi Xin Liu, Heidi Feigenbaum, Samaneh Bayati, Winston Wang, Jennifer Wade, Husain Mithaiwala, Matthew D. Green

Abstract: A new direct air capture (DAC) technology uses a moisture swing (MS) process with anion exchange membranes, potentially offering a more energy-efficient way to remove CO2 from the air. In this MS process, the membrane absorbs CO2 as it dries and releases it when water is added. Understanding the mechanical behavior of these membranes is essential for improving the design and efficiency of DAC syst… ▽ More A new direct air capture (DAC) technology uses a moisture swing (MS) process with anion exchange membranes, potentially offering a more energy-efficient way to remove CO2 from the air. In this MS process, the membrane absorbs CO2 as it dries and releases it when water is added. Understanding the mechanical behavior of these membranes is essential for improving the design and efficiency of DAC systems and prolonging sorbent lifetime. This study tested one anion exchange membrane, Fumasep FAA-3, under mechanical loading and various temperature and humidity conditions to measure its swelling, stiffness, strength, plastic deformation, and stress relaxation. Experimental results were used to identify a mechanical model for FAA-3 that can be used to predict the material's nonlinear viscous behavior under various loads and environments. △ Less

Submitted 3 August, 2025; originally announced August 2025.

Learning Radical Excited States from Sparse Data

Authors: Jingkun Shen, Lucy E. Walker, Kevin Ma, James D. Green, Hugo Bronstein, Keith T. Butler, Timothy J. H. Hele

Abstract: Emissive organic radicals are currently of great interest for their potential use in the next generation of highly efficient organic light emitting diode (OLED) devices and as molecular qubits. However, simulating their optoelectronic properties is challenging, largely due to spin-contamination and the multireference character of their excited states. Here we present a data-driven approach where,… ▽ More Emissive organic radicals are currently of great interest for their potential use in the next generation of highly efficient organic light emitting diode (OLED) devices and as molecular qubits. However, simulating their optoelectronic properties is challenging, largely due to spin-contamination and the multireference character of their excited states. Here we present a data-driven approach where, for the first time, the excited electronic states of organic radicals are learned directly from experimental excited state data, using a much smaller amount of data than typically required by Machine Learning. We adopt ExROPPP, a fast and spin-pure semiempirical method for calculation of the excited states of radicals, as a surrogate physical model for which we learn the optimal set of parameters. To achieve this we compile the largest known database of organic radical geometries and their UV-vis data, which we use to train our model. Our trained model gives Root Mean Square (RMS) and mean absolute errors for excited state energies of 0.24 and 0.16 eV respectively, improving hugely over ExROPPP with literature parameters. Four new organic radicals are synthesised and we test the model on their spectra, finding even lower errors and similar correlation as for the testing set. This model paves the way for the high throughput discovery of next generation radical-based optoelectronics. △ Less

Submitted 12 June, 2025; v1 submitted 13 December, 2024; originally announced December 2024.

Non-Abelian Combinatorial Gauge Theory

Authors: Hongji Yu, Dmitry Green, Claudio Chamon

Abstract: Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a perturbative regime. This paper extends the framework to encompass generic non-Abelian finite gauge groups by expanding on previous work that developed the theory for… ▽ More Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a perturbative regime. This paper extends the framework to encompass generic non-Abelian finite gauge groups by expanding on previous work that developed the theory for finite Abelian gauge groups and presented one non-Abelian example. △ Less

Submitted 5 November, 2024; originally announced November 2024.

Cooper-pair splitters as circuit elements for realizing topological superconductors

Authors: Guilherme Delfino, Dmitry Green, Saulius Vaitiekėnas, Charles M. Marcus, Claudio Chamon

Abstract: Advances in materials and fabrication of superconducting devices allows the exploration of novel quantum effects in synthetic superconducting systems beyond conventional Josephson junction arrays. As an example, we introduce a new circuit element, the Y-splitter, a superconducting loop with three leads and three Josephson junctions, smaller or comparable in size to the superconducting coherence le… ▽ More Advances in materials and fabrication of superconducting devices allows the exploration of novel quantum effects in synthetic superconducting systems beyond conventional Josephson junction arrays. As an example, we introduce a new circuit element, the Y-splitter, a superconducting loop with three leads and three Josephson junctions, smaller or comparable in size to the superconducting coherence length of the material. By tuning magnetic flux through an array of Y-splitters, Cooper-pair transport can be made to interfere destructively, while spatially separated split Cooper pairs propagate coherently. We consider an array of Y-splitters connected in a two-dimensional star [Archimedean (3,$12^2$)] geometry, deformable into the kagome lattice, and find a rich phase diagram that includes topological superconducting phases with Chern numbers $\pm 2$. Experimental realization appears feasible. △ Less

Submitted 21 September, 2025; v1 submitted 12 August, 2024; originally announced August 2024.

Comments: 19 pages, 18 figures. v2: Added Appendix A which explores the transport properties of a single Cooper-pair splitter

Journal ref: PRX Quantum 6 (2025), 030318

Levin-Wen is a gauge theory: entanglement from topology

Authors: Kyle Kawagoe, Corey Jones, Sean Sanford, David Green, David Penneys

Abstract: We show that the Levin-Wen model of a unitary fusion category $\mathcal{C}$ is a gauge theory with gauge symmetry given by the tube algebra $\operatorname{Tube}(\mathcal{C})$. In particular, we define a model corresponding to a $\operatorname{Tube}(\mathcal{C})$ symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case… ▽ More We show that the Levin-Wen model of a unitary fusion category $\mathcal{C}$ is a gauge theory with gauge symmetry given by the tube algebra $\operatorname{Tube}(\mathcal{C})$. In particular, we define a model corresponding to a $\operatorname{Tube}(\mathcal{C})$ symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case $\mathcal{C}=\mathsf{Hilb}(G,ω)$, we show how our procedure reduces to the twisted gauging of a trivial $G$-SPT to produce the Twisted Quantum Double. We further provide an example which is outside the bounds of the current literature, the trivial Fibonacci SPT, whose gauge theory results in the doubled Fibonacci string-net. Our formalism has a natural topological interpretation with string diagrams living on a punctured sphere. We provide diagrams to supplement our mathematical proofs and to give the reader an intuitive understanding of the subject matter. △ Less

Submitted 24 January, 2024; originally announced January 2024.

Comments: 16 pages, 1 figure

MSC Class: 81V27; 18M30 (primary) 18M20; 46L60; 57R56; 81T05; 81T25 (secondary)

Enriched string-net models and their excitations

Authors: David Green, Peter Huston, Kyle Kawagoe, David Penneys, Anup Poudel, Sean Sanford

Abstract: Boundaries of Walker-Wang models have been used to construct commuting projector models which realize chiral unitary modular tensor categories (UMTCs) as boundary excitations. Given a UMTC $\mathcal{A}$ representing the Witt class of an anomaly, the article [arXiv:2208.14018] gave a commuting projector model associated to an $\mathcal{A}$-enriched unitary fusion category $\mathcal{X}$ on a 2D boun… ▽ More Boundaries of Walker-Wang models have been used to construct commuting projector models which realize chiral unitary modular tensor categories (UMTCs) as boundary excitations. Given a UMTC $\mathcal{A}$ representing the Witt class of an anomaly, the article [arXiv:2208.14018] gave a commuting projector model associated to an $\mathcal{A}$-enriched unitary fusion category $\mathcal{X}$ on a 2D boundary of the 3D Walker-Wang model associated to $\mathcal{A}$. That article claimed that the boundary excitations were given by the enriched center/Müger centralizer $Z^\mathcal{A}(\mathcal{X})$ of $\mathcal{A}$ in $Z(\mathcal{X})$. In this article, we give a rigorous treatment of this 2D boundary model, and we verify this assertion using topological quantum field theory (TQFT) techniques, including skein modules and a certain semisimple algebra whose representation category describes boundary excitations. We also use TQFT techniques to show the 3D bulk point excitations of the Walker-Wang bulk are given by the Müger center $Z_2(\mathcal{A})$, and we construct bulk-to-boundary hopping operators $Z_2(\mathcal{A})\to Z^{\mathcal{A}}(\mathcal{X})$ reflecting how the UMTC of boundary excitations $Z^{\mathcal{A}}(\mathcal{X})$ is symmetric-braided enriched in $Z_2(\mathcal{A})$. This article also includes a self-contained comprehensive review of the Levin-Wen string net model from a unitary tensor category viewpoint, as opposed to the skeletal $6j$ symbol viewpoint. △ Less

Submitted 19 March, 2024; v1 submitted 23 May, 2023; originally announced May 2023.

Comments: 43 pages; numerous figures

MSC Class: 18M20 (Primary) 81V27; 18M30; 57R56 (Secondary)

Journal ref: Quantum 8, 1301 (2024)

Many-body Theory Calculations of Positron Binding to Halogenated Hydrocarbons

Authors: J. P. Cassidy, J. Hofierka, B. Cunningham, C. M. Rawlins, C. H. Patterson, D. G. Green

Abstract: Positron binding energies in halogenated hydrocarbons are calculated \emph{ab initio} using many-body theory. For chlorinated molecules, including planars for which the interaction is highly anisotropic, very good to excellent agreement with experiment and recent DFT-based model-potential calculations is found. Predictions for fluorinated and brominated molecules are presented. The comparative eff… ▽ More Positron binding energies in halogenated hydrocarbons are calculated \emph{ab initio} using many-body theory. For chlorinated molecules, including planars for which the interaction is highly anisotropic, very good to excellent agreement with experiment and recent DFT-based model-potential calculations is found. Predictions for fluorinated and brominated molecules are presented. The comparative effect of fluorination, chlorination and bromination is elucidated by identifying trends within molecular families including dihaloethylenes and halomethanes based on global molecular properties (dipole moment, polarizability, ionization energy). It is shown that relative to brominated and chlorinated molecules, fluorinated molecules generate a less attractive positron-molecule potential due to larger ionization energies and smaller density of molecular orbitals close to the HOMO, resulting in very weak, or in most cases loss of, positron binding. Overall, however, it is shown that the global molecular properties are not universal predictors of binding energies, exemplified by consideration of CH$_3$Cl vs.~\emph{cis.}-C$_2$H$_2$F$_2$: despite the latter having a larger dipole moment, lower ionization energy and similar polarizability its binding energy is significantly smaller (25 meV vs.~3 meV, respectively), owing to the important contribution of multiple molecular orbitals to, and the anisotropy of, the positron-molecule correlation potential. △ Less

Submitted 20 December, 2023; v1 submitted 9 March, 2023; originally announced March 2023.

Comments: 5 pages, with additional 4 supplemental pages

Journal ref: Phys. Rev. A Letter 109 L040801 (2024)

A lattice model for condensation in Levin-Wen systems

Authors: Jessica Christian, David Green, Peter Huston, David Penneys

Abstract: Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the {Drinfeld} center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensa… ▽ More Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the {Drinfeld} center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase. △ Less

Submitted 14 March, 2023; v1 submitted 8 March, 2023; originally announced March 2023.

Comments: 45 pages; numerous figures

MSC Class: 18M20 (Primary) 81V27; 18M30; 57R56 (Secondary)

Many-Body Theory Calculations of Positron Scattering and Annihilation in H$_2$, N$_2$ and CH$_4$

Authors: C. M. Rawlins, J. Hofierka, B. Cunningham, C. H. Patterson, D. G. Green

Abstract: The recently developed ab initio many-body theory of positron molecule binding [J. Hofierka et al., Nature, 606, 688 (2022)] is combined with the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)] to calculate positron scattering and annihilation rates on small molecules, namely H$_2$, N$_2$ and CH$_4$. The important effects of positron-molecule correlati… ▽ More The recently developed ab initio many-body theory of positron molecule binding [J. Hofierka et al., Nature, 606, 688 (2022)] is combined with the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)] to calculate positron scattering and annihilation rates on small molecules, namely H$_2$, N$_2$ and CH$_4$. The important effects of positron-molecule correlations are delineated. The method provides uniformly good results for annihilation rates on all the targets, from the simplest (H$_2$, for which only a sole previous calculation agrees with experiment), to larger targets, where high-quality calculations have not been available. △ Less

Submitted 3 March, 2023; originally announced March 2023.

Comments: Main text and Supplemental Material

Journal ref: Phys. Rev. Lett. 130, 263001 (2023)

$U(1)$ symmetry-enriched toric code

Authors: Kai-Hsin Wu, Alexey Khudorozhkov, Guilherme Delfino, Dmitry Green, Claudio Chamon

Abstract: We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state manifold with indications of UV/IR mixing, i.e., the topological degeneracy of the ground state depends on the microscopic details of the lattice. Specifically… ▽ More We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state manifold with indications of UV/IR mixing, i.e., the topological degeneracy of the ground state depends on the microscopic details of the lattice. Specifically, the ground state degeneracy depends on the lattice tilt relative to the directions of the torus cycles. In particular, we observe that while the usual compactification along the vertical/horizontal lines of the square lattice shows a two-fold ground state degeneracy, compactifying the lattice at $45^\circ$ leads to a three-fold degeneracy. In addition to its unusual topological properties, this system also exhibits Hilbert space fragmentation. Finally, we propose a candidate experimental realization of the model in an array of superconducting quantum wires. △ Less

Submitted 17 May, 2023; v1 submitted 7 February, 2023; originally announced February 2023.

Abelian combinatorial gauge symmetry

Authors: Hongji Yu, Dmitry Green, Andrei E. Ruckenstein, Claudio Chamon

Abstract: Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction… ▽ More Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction to any finite Abelian group. In addition to the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians. △ Less

Submitted 26 September, 2023; v1 submitted 7 December, 2022; originally announced December 2022.

Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Authors: Dmitry Green, Claudio Chamon

Abstract: We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic $ZZ$ interactions, plus longitudinal and transverse fields, and therefore is an explicit example o… ▽ More We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic $ZZ$ interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry. △ Less

Submitted 19 March, 2023; v1 submitted 28 September, 2022; originally announced September 2022.

Comments: 9 pages, 4 figures. Minor edits to make exposition clearer in some places

Journal ref: SciPost Phys. 15, 067 (2023)

B-Spline basis Hartree-Fock method for arbitrary central potentials: atoms, clusters and electron gas

Authors: D. T. Waide, D. G. Green, G. F. Gribakin

Abstract: An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline basis in a finite-size box. Convergence of the self-consistency iterations for the occupied electron orbitals is achieved by increasing the magnitude of the el… ▽ More An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline basis in a finite-size box. Convergence of the self-consistency iterations for the occupied electron orbitals is achieved by increasing the magnitude of the electron-electron Coulomb interaction gradually to its true value. For the Coulomb central potential, convergence patterns and energies are presented for a selection of atoms and negative ions, and are benchmarked against existing calculations. The present approach is also tested by calculating the ground states for an electron gas confined by a harmonic potential and also by that of uniformly charged sphere (the jellium model of alkali-metal clusters). For the harmonically confined electron-gas problem, comparisons are made with the Thomas-Fermi method and its accurate asymptotic analytical solution, with close agreement found for the electron energy and density for large electron numbers. We test the accuracy and effective completeness of the excited state manifolds by calculating the static dipole polarizabilities at the HF level and using the Random-Phase Approximation. Using the latter is crucial for the electron-gas and cluster models, where the effect of electron screening is very important. Comparisons are made for with experimental data for sodium clusters of up to $\sim $100 atoms. △ Less

Submitted 12 August, 2021; originally announced August 2021.

Comments: 21 pages, 10 figures

Many-body theory of positron binding in polyatomic molecules

Authors: J. Hofierka, B. Cunningham, C. M. Rawlins, C. H. Patterson, D. G. Green

Abstract: Positrons bind to molecules leading to vibrational excitation and spectacularly enhanced annihilation. Whilst positron binding energies have been measured via resonant annihilation spectra for $\sim$90 molecules in the past two decades, an accurate \emph{ab initio} theoretical description has remained elusive. Of the molecules studied experimentally, calculations exist for only 6, and for these, s… ▽ More Positrons bind to molecules leading to vibrational excitation and spectacularly enhanced annihilation. Whilst positron binding energies have been measured via resonant annihilation spectra for $\sim$90 molecules in the past two decades, an accurate \emph{ab initio} theoretical description has remained elusive. Of the molecules studied experimentally, calculations exist for only 6, and for these, standard quantum chemistry approaches have proved severely deficient, agreeing with experiment to at best 25% accuracy for polar molecules, and failing to predict binding in nonpolar molecules. The mechanisms of binding are not understood. Here, we develop a many-body theory of positron-molecule interactions and uncover the role of strong many-body correlations including polarization of the electron cloud, screening of the positron-electron Coulomb interaction by molecular electrons, and crucially, the unique non-perturbative process of virtual-positronium formation (where a molecular electron temporarily tunnels to the positron): they dramatically enhance binding in polar molecules and enable binding in nonpolars. We also elucidate the role of individual molecular orbitals, highlighting the importance of electronic $π$ bonds. Overall, we calculate binding energies in agreement with experiment (to within 1% in cases), and we predict binding in formamide and nucleobases. As well as supporting resonant annihilation experiments and positron-based molecular spectroscopy, the approach can be extended to positron scattering and annihilation $γ$ spectra in molecules and condensed matter, to provide fundamental insight and predictive capability required to properly interpret materials science diagnostics, develop antimatter-based technologies (including positron traps, beams and positron emission tomography), and understand positrons in the galaxy. △ Less

Submitted 12 July, 2021; v1 submitted 14 May, 2021; originally announced May 2021.

Comments: Significantly updated: improved calculation now gives near-exact agreement with experiment for some molecules (within 1% in some cases); strength of correlation potential has been delineated; contribution of individual molecular orbitals (including pi-bonds) to binding and annihilation has been elucidated etc

Journal ref: Nature, 606, 688 (2022)

Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

Authors: Kai-Hsin Wu, Zhi-Cheng Yang, Dmitry Green, Anders W. Sandvik, Claudio Chamon

Abstract: We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our si… ▽ More We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions. △ Less

Submitted 30 March, 2021; originally announced March 2021.

Journal ref: Phys. Rev. B 104, 085145 (2021)

$\mathbb{Z}_3$ quantum double in a superconducting wire array

Authors: Zhi-Cheng Yang, Dmitry Green, Hongji Yu, Claudio Chamon

Abstract: We show that a $\mathbb{Z}_3$ quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the inter-wire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry -- a local $\mathbb{Z}_3$ symmetry involving permutations and shifts by $\pm 2π/3$ of… ▽ More We show that a $\mathbb{Z}_3$ quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the inter-wire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry -- a local $\mathbb{Z}_3$ symmetry involving permutations and shifts by $\pm 2π/3$ of the superconducting phases. The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the non-zero flux sectors. A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a $\mathbb{Z}_3$ topologically ordered state. Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term. We further show that our model maps to a quantum three-state Potts model under a duality transformation. We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the $\mathbb{Z}_3$ topological phase into a quantum XY-ordered phase. Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions. △ Less

Submitted 13 August, 2021; v1 submitted 5 January, 2021; originally announced January 2021.

Comments: Updated to published version

Journal ref: PRX Quantum 2, 030327 (2021)

Experimental Realization of Classical $\mathbb{Z}_2$ Spin Liquids in a Programmable Quantum Device

Authors: Shiyu Zhou, Dmitry Green, Edward D. Dahl, Claudio Chamon

Abstract: We build and probe a $\mathbb{Z}_2$ spin liquid in a programmable quantum device, the D-Wave DW-2000Q. Specifically, we observe the classical 8-vertex and 6-vertex (spin ice) states and transitions between them. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry using only pairwise-qubit interactions and a transverse field, i.e., interactions which are acces… ▽ More We build and probe a $\mathbb{Z}_2$ spin liquid in a programmable quantum device, the D-Wave DW-2000Q. Specifically, we observe the classical 8-vertex and 6-vertex (spin ice) states and transitions between them. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry using only pairwise-qubit interactions and a transverse field, i.e., interactions which are accessible in this quantum device. The combinatorial gauge symmetry remains exact along the full quantum annealing path, landing the system onto the classical 8-vertex model at the endpoint of the path. The output configurations from the device allows us to directly observe the loop structure of the classical model. Moreover, we deform the Hamiltonian so as to vary the weights of the 8 vertices and show that we can selectively attain the classical 6-vertex (ice) model, or drive the system into a ferromagnetic state. We present studies of the classical phase diagram of the system as function of the 8-vertex deformations and effective temperature, which we control by varying the relative strengths of the programmable couplings, and we show that the experimental results are consistent with theoretical analysis. Finally, we identify additional capabilities that, if added to these devices, would allow us to realize $\mathbb{Z}_2$ quantum spin liquids on which to build topological qubits. △ Less

Submitted 17 August, 2021; v1 submitted 16 September, 2020; originally announced September 2020.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. B 104, 081107 (2021)

A superconducting circuit realization of combinatorial gauge symmetry

Authors: Claudio Chamon, Dmitry Green, Andrew J. Kerman

Abstract: We propose a superconducting quantum circuit based on a general symmetry principle -- combinatorial gauge symmetry -- designed to emulate topologically-ordered quantum liquids and serve as a foundation for the construction of topological qubits. The proposed circuit exhibits rich features: in the classical limit of large capacitances its ground state consists of two superimposed loop structures; o… ▽ More We propose a superconducting quantum circuit based on a general symmetry principle -- combinatorial gauge symmetry -- designed to emulate topologically-ordered quantum liquids and serve as a foundation for the construction of topological qubits. The proposed circuit exhibits rich features: in the classical limit of large capacitances its ground state consists of two superimposed loop structures; one is a crystal of small loops containing disordered $U(1)$ degrees of freedom, and the other is a gas of loops of all sizes associated to $\mathbb{Z}_2$ topological order. We show that these classical results carry over to the quantum case, where phase fluctuations arise from the presence of finite capacitances, yielding ${\mathbb Z}_2$ quantum topological order. A key feature of the exact gauge symmetry is that amplitudes connecting different ${\mathbb Z}_2$ loop states arise from paths having zero classical energy cost. As a result, these amplitudes are controlled by dimensional confinement rather than tunneling through energy barriers. We argue that this effect may lead to larger energy gaps than previous proposals which are limited by such barriers, potentially making it more likely for a topological phase to be experimentally observable. Finally, we discuss how our superconducting circuit realization of combinatorial gauge symmetry can be implemented in practice. △ Less

Submitted 8 June, 2021; v1 submitted 17 June, 2020; originally announced June 2020.

Comments: Joined by new author. Added section on experimental realization. Added analytical results

Journal ref: PRX Quantum 2, 030341 (2021)

Exfoliation of Two-Dimensional Nanosheets of Metal Diborides

Authors: Ahmed Yousaf, Matthew S. Gilliam, Shery L. Y. Chang, Mathias Augustin, Yuqi Guo, Fraaz Tahir, Meng Wang, Alexandra Schwindt, Ximo S. Chu, Duo O. Li, Suneet Kale, Abhishek Debnath, Yongming Liu, Matthew D. Green, Elton J. G. Santos, Alexander A. Green, Qing Hua Wang

Abstract: The metal diborides are a class of ceramic materials with crystal structures consisting of hexagonal sheets of boron atoms alternating with planes of metal atoms held together with mixed character ionic/covalent bonds. Many of the metal diborides are ultrahigh temperature ceramics like HfB$_2$, TaB$_2$, and ZrB$_2$, which have melting points above 3000$^\circ$C, high mechanical hardness and streng… ▽ More The metal diborides are a class of ceramic materials with crystal structures consisting of hexagonal sheets of boron atoms alternating with planes of metal atoms held together with mixed character ionic/covalent bonds. Many of the metal diborides are ultrahigh temperature ceramics like HfB$_2$, TaB$_2$, and ZrB$_2$, which have melting points above 3000$^\circ$C, high mechanical hardness and strength at high temperatures, and high chemical resistance, while MgB$_2$ is a superconductor with a transition temperature of 39 K. Here we demonstrate that this diverse family of non-van der Waals materials can be processed into stable dispersions of two-dimensional (2D) nanosheets using ultrasonication-assisted exfoliation. We generate 2D nanosheets of the metal diborides AlB$_2$, CrB$_2$, HfB$_2$, MgB$_2$, NbB$_2$, TaB$_2$, TiB$_2$, and ZrB$_2$, and use electron and scanning probe microscopies to characterize their structures, morphologies, and compositions. The exfoliated layers span up to micrometers in lateral dimension and reach thicknesses down to 2-3 nm, while retaining their hexagonal atomic structure and chemical composition. We exploit the convenient solution-phase dispersions of exfoliated CrB$_2$ nanosheets to incorporate them directly into polymer composites. In contrast to the hard and brittle bulk CrB$_2$, we find that CrB$_2$ nanocomposites remain very flexible and simultaneously provide increases in the elastic modulus and the ultimate tensile strength of the polymer. The successful liquid-phase production of 2D metal diborides enables their processing using scalable low-temperature solution-phase methods, extending their use to previously unexplored applications, and reveals a new family of non-van der Waals materials that can be efficiently exfoliated into 2D forms. △ Less

Submitted 24 January, 2020; originally announced January 2020.

Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Authors: Claudio Chamon, Dmitry Green, Zhi-Cheng Yang

Abstract: We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the com… ▽ More We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated to the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits. △ Less

Submitted 8 August, 2020; v1 submitted 13 August, 2019; originally announced August 2019.

Comments: Updated to published version

Journal ref: Phys. Rev. Lett. 125, 067203 (2020)

Imaging Quasi-Periodic Electronic States in a Synthetic Penrose Tiling

Authors: Laura C. Collins, Thomas G. Witte, Rochelle Silverman, David B. Green, Kenjiro K. Gomes

Abstract: Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the absence of periodicity and the presence of quasicrystalline order, the ways that electronic states change remain a mystery. Scanning tunneling microscopy and atomi… ▽ More Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the absence of periodicity and the presence of quasicrystalline order, the ways that electronic states change remain a mystery. Scanning tunneling microscopy and atomic manipulation can be used to assemble a two-dimensional quasicrystalline structure mapped upon the Penrose tiling. Here, carbon monoxide molecules are arranged on the surface of Cu(111) one at a time to form the potential landscape that mimics the ionic potential of atoms in natural materials by constraining the electrons in the two-dimensional surface state of Cu(111). The real-space images reveal the presence of the quasiperiodic order in the electronic wave functions and the Fourier analysis of our results links the energy of the resonant states to the local vertex structure of the quasicrystal. △ Less

Submitted 20 July, 2017; originally announced July 2017.

Comments: Main text: 14 pages, 4 figures; Supplement: 5 pages, 4 figures

Journal ref: Nature Communications 8, 15961 (2017)

The approach to chaos in ultracold atomic and molecular physics: statistics of near-threshold bound states for Li+CaH and Li+CaF

Authors: Matthew D. Frye, Masato Morita, Christophe L. Vaillant, Dermot G. Green, Jeremy M. Hutson

Abstract: We calculate near-threshold bound states and Feshbach resonance positions for atom + rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum $J=0$ we find fully chaotic behavior in both the nearest-neighbor spacing distribution a… ▽ More We calculate near-threshold bound states and Feshbach resonance positions for atom + rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum $J=0$ we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for $J>0$ we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF ($J=0$) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. We suggest this may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior. △ Less

Submitted 21 April, 2016; v1 submitted 27 November, 2015; originally announced November 2015.

Comments: 13 pages, 10 figures

Journal ref: Phys. Rev. A 93, 052713 (2016)

Quantum chaos in ultracold collisions between Yb($^1$S$_0$) and Yb($^3$P$_2$)

Authors: Dermot G. Green, Christophe L. Vaillant, Matthew D. Frye, Masato Morita, Jeremy M. Hutson

Abstract: We calculate and analyze Feshbach resonance spectra for ultracold Yb($^1$S$_0$) + Yb($^3$P$_2$) collisions as a function of an interatomic potential scaling factor $λ$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $λ$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superpositio… ▽ More We calculate and analyze Feshbach resonance spectra for ultracold Yb($^1$S$_0$) + Yb($^3$P$_2$) collisions as a function of an interatomic potential scaling factor $λ$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $λ$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances in magnetic field in the experimentally accessible range 400 to 2000~G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos. △ Less

Submitted 4 February, 2016; v1 submitted 23 October, 2015; originally announced October 2015.

Comments: 5 Pages, 3 figures. Data available at doi:10.15128/ns0646000

Journal ref: Phys. Rev. A 93, 022703 (2016)

High Overtone Quasinormal Modes of Analog Black Holes and the Small Scale Structure of the Background Fluid

Authors: Ramin G. Daghigh, Michael D. Green

Abstract: The goal of this paper is to build a foundation for, and explore the possibility of, using high overtone quasinormal modes of analog black holes to probe the small scale (microscopic) structure of a background fluid in which an analog black hole is formed. This may provide a tool to study the small scale structure of some interesting quantum systems such as Bose-Einstein condensates. In order to b… ▽ More The goal of this paper is to build a foundation for, and explore the possibility of, using high overtone quasinormal modes of analog black holes to probe the small scale (microscopic) structure of a background fluid in which an analog black hole is formed. This may provide a tool to study the small scale structure of some interesting quantum systems such as Bose-Einstein condensates. In order to build this foundation, we first look into the hydrodynamic case where we calculate the high overtone quasinormal mode frequencies of a 3+1 dimensional canonical non-rotating acoustic black hole. The leading order calculations have been done earlier in the literature. Here, we obtain the first order correction. We then analyze the high overtone quasinormal modes of acoustic black holes in a Bose-Einstein condensate using the linearized Gross-Pitaevskii equation. We point out that at the high overtone quasinormal mode limit, the only term that is important in the linearized Gross-Pitaevskii equation is the quantum potential term, which is a small scale effect. △ Less

Submitted 25 November, 2014; originally announced November 2014.

Comments: 14 pages, 3 figures

$γ$-ray spectra and enhancement factors for positron annihilation spectra with core-electrons

Authors: D. G. Green, G. F. Gribakin

Abstract: Many-body theory is developed to calculate the $γ$-spectra for positron annihilation with valence and core electrons in the noble gas atoms. A proper inclusion of correlation effects and core annihilation provides for an accurate description of the measured spectra [Iwata \textit{et al.}, Phys. Rev. Lett. {\bf 79}, 39 (1997)]. The theory enables us to calculate the enhancement factors $γ_{nl}$, wh… ▽ More Many-body theory is developed to calculate the $γ$-spectra for positron annihilation with valence and core electrons in the noble gas atoms. A proper inclusion of correlation effects and core annihilation provides for an accurate description of the measured spectra [Iwata \textit{et al.}, Phys. Rev. Lett. {\bf 79}, 39 (1997)]. The theory enables us to calculate the enhancement factors $γ_{nl}$, which describe the effect of electron-positron correlations for annihilation on individual electron orbitals $nl$. We find that the enhancement factors scale with the orbital ionization energy $I_{nl}$ (in electron-volt), as $γ_{nl}=1+\sqrt{A/I_{nl}}+(B/I_{nl})^β$, where $A\approx 40$~eV, $B\approx 24$~eV and $β\approx 2.3$. △ Less

Submitted 7 January, 2015; v1 submitted 17 June, 2014; originally announced June 2014.

Comments: 5 pages, 5 figures

Journal ref: Phys. Rev. Lett. 114, 093201 (2015)

Networks of quantum wire junctions: a system with quantized integer Hall resistance without vanishing longitudinal resistivity

Authors: Jaime Medina, Dmitry Green, Claudio Chamon

Abstract: We consider a honeycomb network built of quantum wires, with each node of the network having a Y-junction of three wires with a ring through which flux can be inserted. The junctions are the basic circuit elements for the network, and they are characterized by 3 x 3 conductance tensors. The low energy stable fixed point tensor conductances result from quantum effects, and are determined by the str… ▽ More We consider a honeycomb network built of quantum wires, with each node of the network having a Y-junction of three wires with a ring through which flux can be inserted. The junctions are the basic circuit elements for the network, and they are characterized by 3 x 3 conductance tensors. The low energy stable fixed point tensor conductances result from quantum effects, and are determined by the strength of the interactions in each wire and the magnetic flux through the ring. We consider the limit where there is decoherence in the wires between any two nodes, and study the array as a network of classical 3-lead circuit elements whose characteristic conductance tensors are determined by the quantum fixed point. We show that this network has some remarkable transport properties in a range of interaction parameters: it has a Hall resistance quantized at Rxy=h/e^2, although the longitudinal resistivity is non-vanishing. We show that these results are robust against disorder, in this case non-homogeneous interaction parameters g for the different wires in the network. △ Less

Submitted 12 February, 2013; v1 submitted 3 October, 2012; originally announced October 2012.

Comments: 8 pages, 8 figures

Journal ref: Physical Review B 87.4 (2013): 045128

Effects of Annealing Conditions on the Microstructure and Magnetic Properties of the Perovskite Manganite, La0.75Sr0.25MnO3

Authors: D. O. J. Green, K-U. Neumann

Abstract: The effects of annealing conditions upon the microstructure and the magnetic properties of the colossal magnetoresistive manganite La0.75Sr0.25MnO3 have been investigated. Increasing the annealing temperature and time of annealing is seen to increase the size of crystallites within the samples. The spontaneous magnetic moment per formula unit and the Curie temperature, as obtained from Arrott plot… ▽ More The effects of annealing conditions upon the microstructure and the magnetic properties of the colossal magnetoresistive manganite La0.75Sr0.25MnO3 have been investigated. Increasing the annealing temperature and time of annealing is seen to increase the size of crystallites within the samples. The spontaneous magnetic moment per formula unit and the Curie temperature, as obtained from Arrott plot analysis, are observed to depend upon the average size of crystallites. △ Less

Submitted 13 May, 2011; originally announced May 2011.

Comments: 6 pages, 6 figures, 1 table

Mapping Colossal Magnetoresistance Phase Transitions with the Charge-Carrier Density Collapse Model

Authors: D. O. J. Green

Abstract: We explain the observed specific heat anomaly (and hence entropy change) in the colossal magnetoresistive manganite Sm0.55Sr0.45MnO3, by introducing phase separation into the current carrier density collapse theory via the notion of the ferromagnetic volume fraction. Within the same framework, we have also been able to explain the observed electrical resistivity of Sm0.55Sr0.45MnO3 by using approp… ▽ More We explain the observed specific heat anomaly (and hence entropy change) in the colossal magnetoresistive manganite Sm0.55Sr0.45MnO3, by introducing phase separation into the current carrier density collapse theory via the notion of the ferromagnetic volume fraction. Within the same framework, we have also been able to explain the observed electrical resistivity of Sm0.55Sr0.45MnO3 by using appropriate expressions governing the scattering mechanisms far away from the transition. Fitting specific heat and resistivity results has allowed us to separate the hopping activation energy of polaronic carriers and the bipolaron binding energy contributions to the exponential behaviour of resistivity in the paramagnetic phase. △ Less

Submitted 12 May, 2011; originally announced May 2011.

Comments: 8 pages, 6 figures, 2 tables

Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices

Authors: Dmitry Green, Luiz Santos, Claudio Chamon

Abstract: Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures that arise in tight-binding Hamiltonians defined on hexagonal and kagome lattices with staggered fluxes. The flat bands and their neighboring dispersing bands… ▽ More Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures that arise in tight-binding Hamiltonians defined on hexagonal and kagome lattices with staggered fluxes. The flat bands and their neighboring dispersing bands have several notable features: (a) Flat bands can be isolated from other bands by breaking time reversal symmetry, allowing for an extensive degeneracy when these bands are partially filled; (b) An isolated flat band corresponds to a critical point between regimes where the band is electron-like or hole-like, with an anomalous Hall conductance that changes sign across the transition; (c) When the gap between a flat band and two neighboring bands closes, the system is described by a single spin-1 conical-like spectrum, extending to higher angular momentum the spin-1/2 Dirac-like spectra in topological insulators and graphene; and (d) some configurations of parameters admit two isolated parallel flat bands, raising the possibility of exotic "heavy excitons"; (e) We find that the Chern number of the flat bands, in all instances that we study here, is zero. △ Less

Submitted 11 August, 2010; v1 submitted 5 April, 2010; originally announced April 2010.

Comments: 7 pages. Sec. II slightly expanded. References added

Journal ref: Phys. Rev. B 82, 075104 (2010)

Boundary Entropy Can Increase Under Bulk RG Flow

Authors: Daniel Green, Michael Mulligan, David Starr

Abstract: The boundary entropy log(g) of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g due to a slightly… ▽ More The boundary entropy log(g) of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy log(g) can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter. △ Less

Submitted 12 November, 2007; v1 submitted 24 October, 2007; originally announced October 2007.

Comments: 20 pages

Report number: SU-ITP-07/19, SLAC-PUB-12907

Journal ref: Nucl.Phys.B798:491-504,2008

Realization of wide electron slabs by polarization bulk doping in graded III-V nitride semiconductor alloys

Authors: Debdeep Jena, Sten Heikman, Daniel Green, Ilan B. Yaacov, Robert Coffie, Huili Xing, Stacia Keller, Steve DenBaars, James S. Speck, Umesh K. Mishra

Abstract: We present the concept and experimental realization of polarization-induced bulk electron doping in III-V nitride semiconductors. By exploiting the large polarization charges in the III-V nitrides, we are able to create wide slabs of high density mobile electrons without introducing shallow donors. Transport measurements reveal the superior properties of the polarization doped electron distribut… ▽ More We present the concept and experimental realization of polarization-induced bulk electron doping in III-V nitride semiconductors. By exploiting the large polarization charges in the III-V nitrides, we are able to create wide slabs of high density mobile electrons without introducing shallow donors. Transport measurements reveal the superior properties of the polarization doped electron distributions than comparable shallow donor doped structures. The technique is readily employed for creating highly conductive layers in many device structures. △ Less

Submitted 22 April, 2002; originally announced April 2002.

Comments: Submitted to Applied Physics Letters

Strongly Correlated States in Low Dimensions (Thesis)

Authors: Dmitry Green

Abstract: This thesis is a theoretical analysis of sample two- and one-dimensional systems. The two-dimensional examples are the quantum Hall liquid and anomalous paired states. The most widely accepted effective theory of the quantum Hall liquid is based on the so-called Chern Simons Lagrangian, but it is not entirely satisfactory. We obtain the first derivation of an alternative effective theory from mi… ▽ More This thesis is a theoretical analysis of sample two- and one-dimensional systems. The two-dimensional examples are the quantum Hall liquid and anomalous paired states. The most widely accepted effective theory of the quantum Hall liquid is based on the so-called Chern Simons Lagrangian, but it is not entirely satisfactory. We obtain the first derivation of an alternative effective theory from microscopic principles. Our formulation allows for a first principles derivation of physical quantities such as the effective mass and compressibility and contains the first analytical observation of the magnetoroton. The formalism developed along the way is also applied to paired states in anomalous supeconductors, a topic of much recent interest. The one-dimenisonal system is the carbon nanotube. Gas uptake in nanotube bundles is currently attracting a wealth of research with both applied and fundamental implications. We propose adsorption of gases on the surface of a single tube, finding strong correlations and symmetries that have not been observed yet. The properties of these states are directly relevant to other one-dimensional structures such as spin ladders and stripes and raise interesting and open questions. △ Less

Submitted 26 February, 2002; originally announced February 2002.

Comments: Chapters 5,6 published. Chapters 2,3,4 to be published in revised form. 135 pages including 20 figures

Journal ref: N. Read and D. Green PRB 61, 10267 (2000); D. Green and C. Chamon, PRL 85, 4128 (2000)

Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes

Authors: Dmitry Green, Claudio Chamon

Abstract: We study XXZ Heisenberg models on frustrated triangular lattices wrapped around a cylinder. In addition to having interesting magnetic phases, these models are equivalent to Bose-Hubbard models that describe the physical problem of adsorption of noble gases on the surface of carbon nanotubes. We find analytical results for the possible magnetization plateau values as a function of the wrapping v… ▽ More We study XXZ Heisenberg models on frustrated triangular lattices wrapped around a cylinder. In addition to having interesting magnetic phases, these models are equivalent to Bose-Hubbard models that describe the physical problem of adsorption of noble gases on the surface of carbon nanotubes. We find analytical results for the possible magnetization plateau values as a function of the wrapping vectors of the cylinder, which in general introduce extra geometric frustration besides the one due to the underlying triangular lattice. We show that for particular wrapping vectors $(N,0)$, which correspond to the zig-zag nanotubes, there is a macroscopically degenerate ground state in the classical Ising limit. The Hilbert space for the degenerate states can be enumerated by a mapping first into a path in a square lattice wrapped around a cylinder (a Bratteli diagram), and then to free fermions interacting with a single ${\bf Z}_N$ degree of freedom. From this model we obtain the spectrum in the anisotropic Heisenberg limit, showing that it is gapless. The continuum limit is a $c=1$ conformal field theory with compactification radius $R=N$ set by the physical tube radius. We show that the compactification radius quantization is exact in the projective $J_\perp/J_z \ll 1$ limit, and that higher order corrections reduce the value of $R$. The particular case of a $(N=2,0)$ tube, which corresponds to a 2-leg ladder with cross links, is studied separately and shown to be gapped because the fermion mapped problem contains superconducting pairing terms. △ Less

Submitted 13 May, 2001; originally announced May 2001.

Comments: 10 pages, 11 figures

Adsorption on carbon nanotubes: quantum spin tubes, magnetization plateaus, and conformal symmetry

Authors: Dmitry Green, Claudio Chamon

Abstract: We formulate the problem of adsorption onto the surface of a carbon nanotube as a lattice gas on a triangular lattice wrapped around a cylinder. This model is equivalent to an XXZ Heisenberg quantum spin tube. The geometric frustration due to wrapping leads generically to four magnetization plateaus, in contrast to the two on a flat graphite sheet. We obtain analytical and numerical results for… ▽ More We formulate the problem of adsorption onto the surface of a carbon nanotube as a lattice gas on a triangular lattice wrapped around a cylinder. This model is equivalent to an XXZ Heisenberg quantum spin tube. The geometric frustration due to wrapping leads generically to four magnetization plateaus, in contrast to the two on a flat graphite sheet. We obtain analytical and numerical results for the magnetizations and transition fields for armchair, zig-zag and chiral nanotubes. The zig-zags are exceptional in that one of the plateaus has extensive zero temperature entropy in the classical limit. Quantum effects lift up the degeneracy, leaving gapless excitations which are described by a $c=1$ conformal field theory with compactification radius quantized by the tube circumference. △ Less

Submitted 18 April, 2000; v1 submitted 18 April, 2000; originally announced April 2000.

Comments: 5 pages, 6 figures

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect

Authors: N. Read, Dmitry Green

Abstract: We analyze pairing of fermions in two dimensions for fully-gapped cases with broken parity (P) and time-reversal (T), especially cases in which the gap function is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$ (p-wave, spinless or spin-triplet) and $l=-2$ (d-wave, spin-singlet). For $l\neq0$, these fall into two phases, weak and strong pairing, which may be distinguished top… ▽ More We analyze pairing of fermions in two dimensions for fully-gapped cases with broken parity (P) and time-reversal (T), especially cases in which the gap function is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$ (p-wave, spinless or spin-triplet) and $l=-2$ (d-wave, spin-singlet). For $l\neq0$, these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless p-wave case, the weak-pairing phase has a pair wavefunction that is asympototically the same as that in the Moore-Read (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole and toroidal ground states) are also the same, indicating that nonabelian statistics is a {\em generic} property of such a paired phase. The strong-pairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the d-wave case, we argue that the Haldane-Rezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weak-pairing phase is an abelian phase which has been considered previously. In the p-wave case with an unbroken U(1) symmetry, which can be applied to the double layer quantum Hall problem, the weak-pairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the Moore-Read phase. The effects of disorder on noninteracting quasiparticles are considered. △ Less

Submitted 23 January, 2000; v1 submitted 30 June, 1999; originally announced June 1999.

Comments: Accepted by PRB; references added and typos corrected

Journal ref: Phys.Rev.B61:10267,2000