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Local Certification of Many-Body Steady States
Authors:
Miguel Frías Pérez,
Antonio Acín
Abstract:
We present a relaxation-based method to bound expectation values on the steady state of dissipative many-body quantum systems described by master equations of the Lindblad form. Instead of targeting to represent the entire state, we promote the reduced density matrices to our variables and enforce the constraints that are imposed on them by consistency with a global steady state. The resulting con…
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We present a relaxation-based method to bound expectation values on the steady state of dissipative many-body quantum systems described by master equations of the Lindblad form. Instead of targeting to represent the entire state, we promote the reduced density matrices to our variables and enforce the constraints that are imposed on them by consistency with a global steady state. The resulting constraints have the form of a semidefinite program, which allows us to efficiently bound the values a given expectation value can take in the steady state. Our results show fast convergence of the bounds with the size of the reduced density matrices, giving very competitive predictions for the steady state of several one- and two-dimensional models for an arbitrary number of particles.
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Submitted 6 February, 2026;
originally announced February 2026.
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Extracting conserved operators from a projected entangled pair state
Authors:
Wen-Tao Xu,
Miguel Frías Pérez,
Mingru Yang
Abstract:
Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically $k$-local conserved operators that have the given infinite projected entangled pair state (iPEPS) in 2D as an (approximate) eigenstate. The key ingredient is the evaluation of the static structu…
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Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically $k$-local conserved operators that have the given infinite projected entangled pair state (iPEPS) in 2D as an (approximate) eigenstate. The key ingredient is the evaluation of the static structure factors of multi-site operators through differentiating the generating function. These generating functions define a manifold of the given tensor network state deformed by some parameters, endowed with a quantum geometry, where conserved operators correspond to vanishing fidelity susceptibility. Despite the approximation errors, we show that our method is still able to extract from exact or variational iPEPS to good precision both frustration-free and non-frustration-free parent Hamiltonians that are beyond the standard construction and obtain better locality. In particular, we find a 4-site-plaquette local Hamiltonian that approximately has the short-range RVB state as the ground state. Moreover, we find a Hamiltonian for which the deformed toric code state at arbitrary string tension is an excited eigenstate with the same energy, thereby potentially realizing quantum many-body scars.
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Submitted 14 April, 2026; v1 submitted 25 November, 2025;
originally announced November 2025.
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Quantum Covariance Scalar Products and Efficient Estimation of Max-Ent Projections
Authors:
F. T. B. Pérez,
J. M. Matera
Abstract:
The maximum-entropy principle (Max-Ent) is a valuable and extensively used tool in statistical mechanics and quantum information theory. It provides a method for inferring the state of a system by utilizing a reduced set of parameters associated with measurable quantities. However, the computational cost of employing Max-Ent projections in simulations of quantum many-body systems is a significant…
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The maximum-entropy principle (Max-Ent) is a valuable and extensively used tool in statistical mechanics and quantum information theory. It provides a method for inferring the state of a system by utilizing a reduced set of parameters associated with measurable quantities. However, the computational cost of employing Max-Ent projections in simulations of quantum many-body systems is a significant drawback, primarily due to the computational cost of evaluating these projections. In this work, a different approach for estimating Max-Ent projections is proposed. The approach involves replacing the expensive Max-Ent induced local geometry, represented by the Kubo-Mori-Bogoliubov (KMB) scalar product, with a less computationally demanding geometry. Specifically, a new local geometry is defined in terms of the quantum analog of the covariance scalar product for classical random variables. Relations between induced distances and projections for both products are explored. Connections with standard variational and dynamical Mean-Field approaches are discussed. The effectiveness of the approach is calibrated and illustrated by its application to the dynamic of excitations in a XX Heisenberg spin-$\frac{1}{2}$ chain model.
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Submitted 29 February, 2024; v1 submitted 17 July, 2023;
originally announced July 2023.
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Computational Determination of the Electronic Structure for different Graphene Quantum Dot geometries
Authors:
Alexander Leon,
Juan E. Gomez,
Freddy R. Perez
Abstract:
The interaction between carbon nanostructures like quantum dots and radiation can generate different effects inside the nanomaterial, with the use of computational methods such effects can be predicted and optimize the material allowing a desired output. In this work, a theoretical model for pristine graphene quantum dots is studied, allowing to explain the shape and size dependence for the electr…
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The interaction between carbon nanostructures like quantum dots and radiation can generate different effects inside the nanomaterial, with the use of computational methods such effects can be predicted and optimize the material allowing a desired output. In this work, a theoretical model for pristine graphene quantum dots is studied, allowing to explain the shape and size dependence for the electronic properties and how the bandgap can be tuned with the functionalization of the nanostructure at the edges.
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Submitted 6 May, 2022;
originally announced May 2022.
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Spin waves in doped graphene: a time-dependent spin-density-functional approach to collective excitations in paramagnetic two-dimensional Dirac fermion gases
Authors:
Matthew J. Anderson,
Florent Perez,
Carsten A. Ullrich
Abstract:
In spin-polarized itinerant electron systems, collective spin-wave modes arise from dynamical exchange and correlation (xc) effects. We here consider spin waves in doped paramagnetic graphene with adjustable Zeeman-type band splitting. The spin waves are described using time-dependent spin-density-functional response theory, treating dynamical xc effects within the Slater and Singwi-Tosi-Land-Sjol…
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In spin-polarized itinerant electron systems, collective spin-wave modes arise from dynamical exchange and correlation (xc) effects. We here consider spin waves in doped paramagnetic graphene with adjustable Zeeman-type band splitting. The spin waves are described using time-dependent spin-density-functional response theory, treating dynamical xc effects within the Slater and Singwi-Tosi-Land-Sjolander approximations. We obtain spin-wave dispersions and spin stiffnesses as a function of doping and spin polarization, and discuss prospects for their experimental observation.
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Submitted 30 September, 2021;
originally announced October 2021.
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Probabilistic Simulation of Quantum Circuits with the Transformer
Authors:
Juan Carrasquilla,
Di Luo,
Felipe Pérez,
Ashley Milsted,
Bryan K. Clark,
Maksims Volkovs,
Leandro Aolita
Abstract:
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to…
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The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasi-stochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits with the Transformer, a powerful ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits which build GHZ and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on six qubits. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.
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Submitted 23 December, 2019;
originally announced December 2019.
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Chirality and intrinsic dissipation of spin modes in two-dimensional electron liquids
Authors:
Irene D'Amico,
Florent Perez,
Carsten A. Ullrich
Abstract:
We review recent theoretical and experimental developments concerning collective spin excitations in two-dimensional electron liquid (2DEL) systems, with particular emphasis on the interplay between many-body and spin-orbit effects, as well as the intrinsic dissipation due to the spin-Coulomb drag. Historically, the experimental realization of 2DELs in silicon inversion layers in the 60s and 70s c…
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We review recent theoretical and experimental developments concerning collective spin excitations in two-dimensional electron liquid (2DEL) systems, with particular emphasis on the interplay between many-body and spin-orbit effects, as well as the intrinsic dissipation due to the spin-Coulomb drag. Historically, the experimental realization of 2DELs in silicon inversion layers in the 60s and 70s created unprecedented opportunities to probe subtle quantum effects, culminating in the discovery of the quantum Hall effect. In the following years, high quality 2DELs were obtained in doped quantum wells made in typical semiconductors like GaAs or CdTe. These systems became important test beds for quantum many-body effects due to Coulomb interaction, spin dynamics, spin-orbit coupling, effects of applied magnetic fields, as well as dissipation mechanisms. Here we focus on the recent results involving chiral effects and intrinsic dissipation of collective spin modes: these are not only of fundamental interest but also important towards demonstrating new concepts in spintronics. Moreover, new realizations of 2DELs are emerging beyond traditional semiconductors, for instance in multilayer graphene, oxide interfaces, dichalcogenide monolayers, and many more. The concepts discussed in this review will be relevant also for these emerging systems.
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Submitted 26 March, 2019; v1 submitted 15 August, 2018;
originally announced August 2018.
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Spin precession and spin waves in a chiral electron gas: beyond Larmor's theorem
Authors:
Shahrzad Karimi,
Florent Baboux,
Florent Perez,
Carsten A. Ullrich,
Grzegorz Karczewski,
Tomasz Wojtowicz
Abstract:
Larmor's theorem holds for magnetic systems that are invariant under spin rotation. In the presence of spin-orbit coupling this invariance is lost and Larmor's theorem is broken: for systems of interacting electrons, this gives rise to a subtle interplay between the spin-orbit coupling acting on individual single-particle states and Coulomb many-body effects. We consider a quasi-two-dimensional, p…
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Larmor's theorem holds for magnetic systems that are invariant under spin rotation. In the presence of spin-orbit coupling this invariance is lost and Larmor's theorem is broken: for systems of interacting electrons, this gives rise to a subtle interplay between the spin-orbit coupling acting on individual single-particle states and Coulomb many-body effects. We consider a quasi-two-dimensional, partially spin-polarized electron gas in a semiconductor quantum well in the presence of Rashba and Dresselhaus spin-orbit coupling. Using a linear-response approach based on time-dependent density-functional theory, we calculate the dispersions of spin-flip waves. We obtain analytic results for small wave vectors and up to second order in the Rashba and Dresselhaus coupling strengths $α$ and $β$. Comparison with experimental data from inelastic light scattering allows us to extract $α$ and $β$ as well as the spin-wave stiffness very accurately. We find significant deviations from the local density approximation for spin-dependent electron systems.
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Submitted 13 December, 2016;
originally announced December 2016.
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Phase diagram of a three-dimensional antiferromagnet with random magnetic anisotropy
Authors:
Felio A. Perez,
Pavel Borisov,
Trent A. Johnson,
Tudor D. Stanescu,
David Lederman,
M. R. Fitzsimmons,
Adam A. Aczel,
Tao Hong
Abstract:
Three-dimensional (3D) antiferromagnets with random magnetic anisotropy (RMA) experimentally studied to date do not have random single-ion anisotropies, but rather have competing two-dimensional and three-dimensional exchange interactions which can obscure the authentic effects of RMA. The magnetic phase diagram Fe$_{x}$Ni$_{1-x}$F$_{2}$ epitaxial thin films with true random single-ion anisotropy…
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Three-dimensional (3D) antiferromagnets with random magnetic anisotropy (RMA) experimentally studied to date do not have random single-ion anisotropies, but rather have competing two-dimensional and three-dimensional exchange interactions which can obscure the authentic effects of RMA. The magnetic phase diagram Fe$_{x}$Ni$_{1-x}$F$_{2}$ epitaxial thin films with true random single-ion anisotropy was deduced from magnetometry and neutron scattering measurements and analyzed using mean field theory. Regions with uniaxial, oblique and easy plane anisotropies were identified. A RMA-induced glass region was discovered where a Griffiths-like breakdown of long-range spin order occurs.
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Submitted 15 December, 2013; v1 submitted 12 December, 2013;
originally announced December 2013.
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Coulomb-driven organization and enhancement of spin-orbit fields in collective spin excitations
Authors:
Florent Baboux,
Florent Perez,
Carsten A. Ullrich,
Irene D'Amico,
Grzegorz Karczewski,
Tomasz Wojtowicz
Abstract:
Spin-orbit (SO) fields in a spin-polarized electron gas are studied by angle-resolved inelastic light scattering on a CdMnTe quantum well. We demonstrate a striking organization and enhancement of SO fields acting on the collective spin excitation (spin-flip wave). While individual electronic SO fields have a broadly distributed momentum dependence, giving rise to D'yakonov-Perel' dephasing, the c…
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Spin-orbit (SO) fields in a spin-polarized electron gas are studied by angle-resolved inelastic light scattering on a CdMnTe quantum well. We demonstrate a striking organization and enhancement of SO fields acting on the collective spin excitation (spin-flip wave). While individual electronic SO fields have a broadly distributed momentum dependence, giving rise to D'yakonov-Perel' dephasing, the collective spin dynamics is governed by a single collective SO field which is drastically enhanced due to many-body effects. The enhancement factor is experimentally determined. These results provide a powerful indication that these constructive phenomena are universal to collective spin excitations of conducting systems.
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Submitted 28 October, 2013;
originally announced October 2013.
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Giant Collective Spin-Orbit Field in a Quantum Well: Fine Structure of Spin Plasmons
Authors:
Florent Baboux,
Florent Perez,
Carsten A. Ullrich,
Irene D'Amico,
Javier Gómez,
Mathieu Bernard
Abstract:
We employ inelastic light scattering with magnetic fields to study intersubband spin plasmons in a quantum well. We demonstrate the existence of a giant collective spin-orbit (SO) field that splits the spin-plasmon spectrum into a triplet. The effect is remarkable as each individual electron would be expected to precess in its own momentum-dependent SO field, leading to D'yakonov-Perel' dephasing.…
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We employ inelastic light scattering with magnetic fields to study intersubband spin plasmons in a quantum well. We demonstrate the existence of a giant collective spin-orbit (SO) field that splits the spin-plasmon spectrum into a triplet. The effect is remarkable as each individual electron would be expected to precess in its own momentum-dependent SO field, leading to D'yakonov-Perel' dephasing. Instead, many-body effects lead to a striking organization of the SO fields at the collective level. The macroscopic spin moment is quantized by a uniform collective SO field, five times higher than the individual SO field. We provide a momentum-space cartography of this field.
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Submitted 28 October, 2013;
originally announced October 2013.
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Effects of hydrogen/deuterium absorption on the magnetic properties of Co/Pd multilayers
Authors:
K. Munbodh,
F. A. Perez,
C. Keenan,
M. Zhernenkov,
M. R. Fitzsimmon,
D. Lederman
Abstract:
The effects of hydrogen (H2) and deuterium (D2) absorption were studied in two Co/Pd multilayers with perpendicular magnetic anisotropy (PMA) using polarized neutron reflectivity (PNR). PNR was measured in an external magnetic field H applied in the plane of the sample with the magnetization M confined in the plane for μ_o H= 6.0 T and partially out of plane at 0.65 T. Nominal thicknesses of the C…
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The effects of hydrogen (H2) and deuterium (D2) absorption were studied in two Co/Pd multilayers with perpendicular magnetic anisotropy (PMA) using polarized neutron reflectivity (PNR). PNR was measured in an external magnetic field H applied in the plane of the sample with the magnetization M confined in the plane for μ_o H= 6.0 T and partially out of plane at 0.65 T. Nominal thicknesses of the Co and Pd layers were 2.5 Å and 21 Å, respectively. Because of these small values, the actual layer chemical composition, thickness, and interface roughness parameters were determined from the nuclear scattering length density profile (ρ_n) and its derivative obtained from both x-ray reflectivity and PNR, and uncertainties were determined using Monte Carlo analysis. The PNR ρ_n showed that although D2 absorption occurred throughout the samples, absorption in the multilayer stack was modest (0.02 D per Pd atom) and thus did not expand. Direct magnetometry showed that H2 absorption decreased the total M at saturation and increased the component of M in the plane of the sample when not at saturation. The PNR magnetic scattering length density (ρ_m) revealed that the Pd layers in the multilayer stack were magnetized and that their magnetization was preferentially modified upon D2 absorption. In one sample, a modulation of M with twice the multilayer period was observed at μ_o H= 0.65 T, which increased upon D2 absorption. These results indicate that H2 or D2 absorption decreases both the PMA and total magnetization of the samples. The lack of measurable expansion during absorption indicates that these changes are primarily governed by modification of the electronic structure of the material.
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Submitted 10 February, 2011;
originally announced February 2011.
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Spin waves in magnetic quantum wells with Coulomb interaction and $sd$ exchange coupling
Authors:
Florent Perez,
Joel Cibert,
Masha Vladimirova,
Denis Scalbert
Abstract:
We theoretically describe the spin excitation spectrum of a two dimensional electron gas embedded in a quantum well with localized magnetic impurities. Compared to the previous work, we introduce equations that allow to consider the interplay between the Coulomb interaction of delocalized electrons and the $sd$ exchange coupling between electrons and magnetic impurities. Strong qualitative changes…
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We theoretically describe the spin excitation spectrum of a two dimensional electron gas embedded in a quantum well with localized magnetic impurities. Compared to the previous work, we introduce equations that allow to consider the interplay between the Coulomb interaction of delocalized electrons and the $sd$ exchange coupling between electrons and magnetic impurities. Strong qualitative changes are found : mixed waves propagate below the single particle continuum, an anticrossing gap is open at a specific wavevector and the kinetic damping due to the electron motion strongly influences the coupling strength between electrons and impurities spins.
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Submitted 19 November, 2010;
originally announced November 2010.
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Dynamical Corrections to Spin Wave Excitations in Quantum Wells due to Coulomb Interactions and Magnetic Ions
Authors:
Cynthia Aku-Leh,
Florent Perez,
Bernard Jusserand,
David Richards,
Grzegorz Karczewski
Abstract:
We have measured dispersions of spin-flip waves and spin-flip single-particle excitations of a spin polarized two-dimensional electron gas in a CdMnTe quantum well using resonant Raman scattering. We find the energy of the spin-flip wave to be below the spin-flip single particle excitation continuum, a contradiction to the theory of spin waves in diluted magnetic semiconductors put forth in [Phys.…
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We have measured dispersions of spin-flip waves and spin-flip single-particle excitations of a spin polarized two-dimensional electron gas in a CdMnTe quantum well using resonant Raman scattering. We find the energy of the spin-flip wave to be below the spin-flip single particle excitation continuum, a contradiction to the theory of spin waves in diluted magnetic semiconductors put forth in [Phys. Rev. B 70, 045205 (2004)]. We show that the inclusion of terms accounting for the Coulomb interaction between carriers in the spin wave propagator leads to an agreement with our experimental results. The dominant Coulomb contribution leads to an overall red shift of the mixed electron-Mn spin modes while the dynamical coupling between Mn ions results in a small blue shift. We provide a simulated model system which shows the reverse situation but at an extremely large magnetic field.
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Submitted 21 August, 2010;
originally announced August 2010.
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Spin polarized two-dimensional electron gas embedded in semimagnetic quantum well : ground state, spin responses, spin excitations, Raman spectrum
Authors:
F. Perez
Abstract:
We present theoretical aspects of spin polarized two dimensional electron gas (SP2DEG) which can be achieved in doped semimagnetic quantum wells. This original model system has been recently studied by magneto Raman scattering experiments has given a new access to spin resolved excitations and spectrum of the SP2DEG. Starting from the Diluted Magnetic Semiconductor (DMS) Hamiltonian in presence…
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We present theoretical aspects of spin polarized two dimensional electron gas (SP2DEG) which can be achieved in doped semimagnetic quantum wells. This original model system has been recently studied by magneto Raman scattering experiments has given a new access to spin resolved excitations and spectrum of the SP2DEG. Starting from the Diluted Magnetic Semiconductor (DMS) Hamiltonian in presence of the Coulomb interaction between conduction electrons, we define the conditions to reach such a SP2DEG. The equilibrium state is studied at low temperature; in particular a theory for the degree of spin polarization is derived. Dynamical spin susceptibilities are further calculated in the framework of a spin density functional formalism already developed in the past. We then derive spin conserving and spin flip excitations dispersions using a recent determination of the SP2DEG correlation energy corrected from the thickness of the well. The SP2DEG presents two key features: the spin flip wave, which existence is a direct consequence of the Coulomb interaction between the spin polarized electrons, with a dispersion and energy range typical to the SP2DEG obtained in DMS, the spin density fluctuations exhibiting a specific collective behaviour when the spin polarization is increased. The dissipation spectrum through these excitations is studied in detail. Particular attention is given to the spectrum determined by resonant Raman scattering. We show, indeed, that the latter gives unique access to the spin-fluctuations spectrum of the SP2DEG.
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Submitted 27 October, 2008;
originally announced October 2008.
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Measuring the spin polarization and Zeeman energy of a spin-polarized electron gas: Comparison between Raman scattering and photoluminescence
Authors:
Cynthia Aku-Leh,
Florent Perez,
Bernard Jusserand,
David Richards,
Wojciech Pacuski,
Piotr Kossacki,
Michel Menant,
Grzegorz Karczewski
Abstract:
We compare resonant electronic Raman scattering and photoluminescence measurements for the characterization of a spin-polarized two-dimensional electron gas embedded in $\text{Cd}_{1-x}\text{Mn}_x\text{Te}$ single quantum wells. From Raman scattering by single-particle excitations in a zero magnetic field, we measure the Fermi velocity and then obtain the Fermi energy (as well as the electron de…
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We compare resonant electronic Raman scattering and photoluminescence measurements for the characterization of a spin-polarized two-dimensional electron gas embedded in $\text{Cd}_{1-x}\text{Mn}_x\text{Te}$ single quantum wells. From Raman scattering by single-particle excitations in a zero magnetic field, we measure the Fermi velocity and then obtain the Fermi energy (as well as the electron density), which is comparable to that extracted from photoluminescence for moderate electron densities, assuming a bare band-edge mass. At large electron densities, the Fermi energies derived from Raman scattering and photoluminescence differ. For an applied in-plane magnetic field and zero wave vector transferred to the electron gas, Raman scattering spectra show peaks at both the Zeeman energy $Z$, resulting from collective excitations of the spin-polarized electron gas, and the one electron spin-flip energy $Z^*$. Magneto-photoluminescence spectra show conduction band splitting that are equivalent to $Z$, suggesting that collective effects are present in the photoluminescence spectra. Assuming (as before) an uncorrected mass, the degree of spin polarization $ζ$ determined from the magneto-photoluminescence lineshape is found to differ from that derived from the magnetic field dependent Raman scattering measurements for large electron densities. We attribute the discrepancy in measuring $ζ$ and the Fermi energy to the renormalized mass resulting from many-body electron-electron interactions.
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Submitted 8 June, 2007;
originally announced June 2007.
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Edge Modes Waves in Superlattices in Quantum Hall Effect Regime
Authors:
Pavel Fileviez Perez,
Alejandro Cabo Montes de Oca,
Carlos Rodriguez Castellanos
Abstract:
The wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along the boundary. The constitutive relations expressing the edge charge and current densities in terms of the fields at the boundary are derived. One of them is s…
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The wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along the boundary. The constitutive relations expressing the edge charge and current densities in terms of the fields at the boundary are derived. One of them is similar to the London equation for superconductor currents. The dispersion relation and wave polarizations for the momenta region $w/c<k$ are also obtained for propagation along the borderlines of the electron gases. It follows that the modes have no dispersion at any frequency. The static limit solutions complete the definition at the boundary of the formerly determined interior field configurations showing a Meissner like effect. The results underline that various of the current theoretical approaches to edge excitations could be appropriate for superlattice structures but can fail to describe standard planar samples.
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Submitted 17 March, 2000; v1 submitted 6 September, 1999;
originally announced September 1999.