Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2406.09985 · Physical review. B./Physical review. B

Spectral and entanglement properties of the random-exchange Heisenberg chain

Yilun Gao, Rudolf A. Römer

Published Mar 7, 2025• 1 citation
arXivHTMLPDF

Abstract

We study the many-body localization problem in the non-Abelian SU(2)-invariant random antiferromagnetic exchange model in 1D. Exact and sparse matrix diagonalization methods are used to calculate eigenvalues and eigenvectors of the Hamiltonian matrix. We investigate the behavior of the energy level gap-ratio statistic, participation ratio, entanglement entropy and the entanglement spectral parameter as a function of disorder strength. Different distributions of random couplings are considered. We find, up to L = 24 , a clear distinction between our non-Abelian model and the more often studied random field Heisenberg model: the regime of seemingly localized behavior is much less pronounced in the random exchange model than in the field model case.

DOI
10.1103/physrevb.111.104202

Related papers

Imperfect many-body localization in exchange-disordered isotropic spin chains

Julian Siegl, John Schliemann

Abstract We investigate many-body localization in isotropic Heisenberg spin chains with the local exchange parameters being subject to quenched disorder. Such systems incorporate a nonabelian symmetry in their Hamiltonian by invariance under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the emergence of a many-body localized phase even in the presence of strong disorder. We report on numerical studies using exact diagonalization for chains of common spin length 1 / 2 and 1. The averaged consecutive-gap ratios display a transition compatible with a crossover from an ergodic phase at small disorder strength to an incompletely localized phase at stronger disorder. Studying the sample-to-sample variance of the averaged consecutive-gap ratio, we distinguish this incompletely localized phase from the fully many-body localized phase by its scaling behavior.

arXiv:2211.04816•New Journal of Physics•Nov 20, 2023•5 citations

Discrete disorder models for many-body localization

Jakub Janarek, Dominique Delande, Jakub Zakrzewski

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

arXiv:1712.03776•Physical review. B./Physical review. B•Apr 16, 2018•28 citations

Probing the randomness of ergodic states: extreme-value statistics in the ergodic and many-body-localized phases

Rajarshi Pal, Arul Lakshminarayan

The extreme-value statistics of the entanglement spectrum in disordered spin chains possessing a many-body localization transition is examined. It is expected that eigenstates in the metallic or ergodic phase, behave as random states and hence the eigenvalues of the reduced density matrix, commonly referred to as the entanglement spectrum, are expected to follow the eigenvalue statistics of a trace normalized Wishart ensemble. In particular, the density of eigenvalues is supposed to follow the universal Marchenko-Pastur distribution. We find deviations in the tails both for the disordered XXZ with total $S_z$ conserved in the half-filled sector as well as in a model that breaks this conservation. A sensitive measure of deviations is provided by the largest eigenvalue, which in the case of the Wishart ensemble after appropriate shift and scaling follows the universal Tracy-Widom distribution. We show that for the models considered, in the metallic phase, the largest eigenvalue of the reduced density matrix of eigenvector, instead follows the generalized extreme-value statistics bordering on the Fisher-Tipett-Gumbel distribution indicating that the correlations between eigenvalues are much weaker compared to the Wishart ensemble. We show by means of distributions conditional on the high entropy and normalized participation ratio of eigenstates that the conditional entanglement spectrum still follows generalized extreme value distribution. In the deeply localized phase we find heavy tailed distributions and Lévy stable laws in an appropriately scaled function of the largest and second largest eigenvalues. The scaling is motivated by a recently developed perturbation theory of weakly coupled chaotic systems.

arXiv:2002.00682•Feb 3, 2020•0 citations

Many-body Localization

Eirik Almklov Magnussen

We study a random-field Heisenberg model numerically and argue that as we vary the strength of the disorder W there is a phase transition between a thermal phase and a many-body localized phase at a critical disorder strength W C = 3.5 ± 1.0.We show some properties of the many-body localized phase and contrast them to the properties of the thermal phase.We have considered transport properties, scaling of entanglement entropy, level statistics, participation ratios and whether or not the system satisfies the ETH to distinguish between the phases.We also study the dynamics in the thermal phase near the transition and argue that the phase transition is governed by an infinite randomness fixed point.Furthermore we review much of what is known and conjectured about the physics of generic closed quantum systems.

•Jan 1, 2017•0 citations

Many Body Localization in 2D Systems with Quasi-Random fields in X and Y Directions

Nicholas Carrillo

Many body localization (MBL) is a phenomena that allows for the preservation of quantum information for long times. We study a variation of the disordered-Heisenberg model, which is known to exhibit an MBL phase [5][6], known as the quasi-Heisenberg model. Our model is a variation of the quasi-Heisenberg model with fields in both x and y directions. We found that while our model shares some characteristics for MBl, as seen by other quasi-Heisenberg models, the adjacent gap ratio for our system falls well below the expected Poisson limit when it transitions to an MBL phase. A similar model to ours has been experimentally realized in [11], and so we are motivated further to study MBL characteristics. To determine the characteristics of the system when transitioning from the ergodic to MBL phase, we calculate the quantities: entanglement entropy, adjacent gap ratio, and the probability distributions for both. We calculate the aforementioned quantities through the eigenvalues and eigenvectors of the system's Hamiltonian, which are obtained through exact diagonalization. We find the entanglement entropy of the system behaves as expected for MBL, with the spectral average of the entanglement entropy dropping close to zero as it enters the MBL phase. However, the spectral average for the adjacent gap ratio falls below the Poisson limit, 0.386, which corresponds to uncorrelated energy levels This drop in adjacent gap ratio can be explained through some level of attraction between energy levels, and is ultimately a consequence of the separability of the quasirandom field. The probability distribution for the adjacent gap ratio is fitted from a derived distribution which was found using the Brody function for energy level spacing. The Brody function accounts for energy level attraction when the Brody parameter, $ω$, becomes negative...

arXiv:1911.11291•Nov 26, 2019•0 citations

Ergodic and non-ergodic properties of disordered SU(3) chains

Bhupen Dabholkar, Fabien Alet

Non-abelian symmetries are thought to be incompatible with many-body localization, but have been argued to produce in certain disordered systems a broad non-ergodic regime distinct from many-body localization. In this context, we present a numerical study of properties of highly-excited eigenstates of disordered chains with SU(3) symmetry. We find that while weakly disordered systems rapidly thermalize, strongly-disordered systems indeed exhibit non-thermal signatures over a large range of system sizes, similar to the one found in previously studied SU(2) systems. Our analysis is based on the spectral, entanglement, and thermalization properties of eigenstates obtained through large-scale exact diagonalization exploiting the full SU(3) symmetry.

arXiv:2403.00442•Mar 1, 2024•0 citations
We study the many-body localization problem in the non-Abelian SU(2)-invariant random antiferromagnetic exchange model in 1D. Exact and sparse matrix diagonalization methods are used to calculate eigenvalues and eigenvectors of the Hamiltonian matrix. We investigate the behavior of the energy level gap-ratio statistic, participation ratio, entanglement entropy and the entanglement spectral parameter as a function of disorder strength. Different distributions of random couplings are considered. We find, up to L = 24 , a clear distinction between our non-Abelian model and the more often studied random field Heisenberg model: the regime of seemingly localized behavior is much less pronounced in the random exchange model than in the field model case.
Abstract We investigate many-body localization in isotropic Heisenberg spin chains with the local exchange parameters being subject to quenched disorder. Such systems incorporate a nonabelian symmetry in their Hamiltonian by invariance under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the emergence of a many-body localized phase even in the presence of strong disorder. We report on numerical studies using exact diagonalization for chains of common spin length 1 / 2 and 1. The averaged consecutive-gap ratios display a transition compatible with a crossover from an ergodic phase at small disorder strength to an incompletely localized phase at stronger disorder. Studying the sample-to-sample variance of the averaged consecutive-gap ratio, we distinguish this incompletely localized phase from the fully many-body localized phase by its scaling behavior.
Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.
The extreme-value statistics of the entanglement spectrum in disordered spin chains possessing a many-body localization transition is examined. It is expected that eigenstates in the metallic or ergodic phase, behave as random states and hence the eigenvalues of the reduced density matrix, commonly referred to as the entanglement spectrum, are expected to follow the eigenvalue statistics of a trace normalized Wishart ensemble. In particular, the density of eigenvalues is supposed to follow the universal Marchenko-Pastur distribution. We find deviations in the tails both for the disordered XXZ with total SzS_zSz​ conserved in the half-filled sector as well as in a model that breaks this conservation. A sensitive measure of deviations is provided by the largest eigenvalue, which in the case of the Wishart ensemble after appropriate shift and scaling follows the universal Tracy-Widom distribution. We show that for the models considered, in the metallic phase, the largest eigenvalue of the reduced density matrix of eigenvector, instead follows the generalized extreme-value statistics bordering on the Fisher-Tipett-Gumbel distribution indicating that the correlations between eigenvalues are much weaker compared to the Wishart ensemble. We show by means of distributions conditional on the high entropy and normalized participation ratio of eigenstates that the conditional entanglement spectrum still follows generalized extreme value distribution. In the deeply localized phase we find heavy tailed distributions and Lévy stable laws in an appropriately scaled function of the largest and second largest eigenvalues. The scaling is motivated by a recently developed perturbation theory of weakly coupled chaotic systems.
We study a random-field Heisenberg model numerically and argue that as we vary the strength of the disorder W there is a phase transition between a thermal phase and a many-body localized phase at a critical disorder strength W C = 3.5 ± 1.0.We show some properties of the many-body localized phase and contrast them to the properties of the thermal phase.We have considered transport properties, scaling of entanglement entropy, level statistics, participation ratios and whether or not the system satisfies the ETH to distinguish between the phases.We also study the dynamics in the thermal phase near the transition and argue that the phase transition is governed by an infinite randomness fixed point.Furthermore we review much of what is known and conjectured about the physics of generic closed quantum systems.
Many body localization (MBL) is a phenomena that allows for the preservation of quantum information for long times. We study a variation of the disordered-Heisenberg model, which is known to exhibit an MBL phase [5][6], known as the quasi-Heisenberg model. Our model is a variation of the quasi-Heisenberg model with fields in both x and y directions. We found that while our model shares some characteristics for MBl, as seen by other quasi-Heisenberg models, the adjacent gap ratio for our system falls well below the expected Poisson limit when it transitions to an MBL phase. A similar model to ours has been experimentally realized in [11], and so we are motivated further to study MBL characteristics. To determine the characteristics of the system when transitioning from the ergodic to MBL phase, we calculate the quantities: entanglement entropy, adjacent gap ratio, and the probability distributions for both. We calculate the aforementioned quantities through the eigenvalues and eigenvectors of the system's Hamiltonian, which are obtained through exact diagonalization. We find the entanglement entropy of the system behaves as expected for MBL, with the spectral average of the entanglement entropy dropping close to zero as it enters the MBL phase. However, the spectral average for the adjacent gap ratio falls below the Poisson limit, 0.386, which corresponds to uncorrelated energy levels This drop in adjacent gap ratio can be explained through some level of attraction between energy levels, and is ultimately a consequence of the separability of the quasirandom field. The probability distribution for the adjacent gap ratio is fitted from a derived distribution which was found using the Brody function for energy level spacing. The Brody function accounts for energy level attraction when the Brody parameter, ωωω, becomes negative...
Non-abelian symmetries are thought to be incompatible with many-body localization, but have been argued to produce in certain disordered systems a broad non-ergodic regime distinct from many-body localization. In this context, we present a numerical study of properties of highly-excited eigenstates of disordered chains with SU(3) symmetry. We find that while weakly disordered systems rapidly thermalize, strongly-disordered systems indeed exhibit non-thermal signatures over a large range of system sizes, similar to the one found in previously studied SU(2) systems. Our analysis is based on the spectral, entanglement, and thermalization properties of eigenstates obtained through large-scale exact diagonalization exploiting the full SU(3) symmetry.