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Localization phenomena in the random XXZ spin chain

Alexander Elgart, Abel Klein

arXiv:2502.01831Journal of Functional AnalysisDec 23, 20250 citations

Dynamical obstruction to localization in a disordered spin chain

Dries Sels, Anatoli Polkovnikov

We analyze a one-dimensional XXZ spin chain in a disordered magnetic field. As the main probes of the system's behavior, we use the sensitivity of eigenstates to adiabatic transformations, as expressed through the fidelity susceptibility, in conjunction with the low-frequency asymptotes of the spectral function. We identify a region of maximal chaos-with exponentially enhanced susceptibility-which separates the many-body localized phase from the diffusive ergodic phase. This regime is characterized by slow transport, and we argue that the presence of such slow dynamics highly constrains any possible localization transition in the thermodynamic limit. Rather, the results are more consistent with absence of the localized phase.We analyze a one-dimensional XXZ spin chain in a disordered magnetic field. As the main probes of the system's behavior, we use the sensitivity of eigenstates to adiabatic transformations, as expressed through the fidelity susceptibility, in conjunction with the low-frequency asymptotes of the spectral function. We identify a region of maximal chaos-with exponentially enhanced susceptibility-which separates the many-body localized phase from the diffusive ergodic phase. This regime is characterized by slow transport, and we argue that the presence of such slow dynamics highly constrains any possible localization transition in the thermodynamic limit. Rather, the results are more consistent with absence of the localized phase.

arXiv:2009.04501Physical review. ENov 8, 2021203 citations

Dynamical Localization in Disordered Quantum Spin Systems

Eman Hamza, Robert Sims, Günter Stolz

arXiv:1108.3811Communications in Mathematical PhysicsAug 1, 201287 citations

Persistence of correlations in many-body localized spin chains

Vasilii Vadimov, Tapio Ala-Nissilä, Mikko Möttönen

We study the evolution and persistence of quantum and classical correlations between spatially separated sites in the disordered XXZ spin chain in its ergodic and many-body-localized phases using exact diagonalization and matrix product state simulations.We show that in the many-body-localized phase, quantum entanglement survives in long-time unitary dynamics of the system, even though it is more fragile than the classical correlations.We study the dependence of the residual entanglement and correlations on the system size and on the disorder strength.Finally, we demonstrate the robustness of entanglement and correlations with respect to local dissipation in the bulk of the system.We study the evolution and persistence of quantum and classical correlations between spatially separated sites in the disordered XXZ spin chain in its ergodic and many-body-localized phases using exact diagonalization and matrix product state simulations.We show that in the many-body-localized phase, quantum entanglement survives in long-time unitary dynamics of the system, even though it is more fragile than the classical correlations.We study the dependence of the residual entanglement and correlations on the system size and on the disorder strength.Finally, we demonstrate the robustness of entanglement and correlations with respect to local dissipation in the bulk of the system.

Physical Review ResearchOct 29, 20200 citations

Many-body delocalization from embedded thermal inclusion

J. Clayton Peacock, Dries Sels

We numerically study quantum avalanches in one-dimensional disordered spin systems by attaching two XXZ spin chains. One chain has low disorder representing a rare Griffith's region, or thermal inclusion, and the second has larger disorder, i.e., disorder larger than the observed finite-size crossover. Comparing dynamics of this system to identical systems with uniformly large disorder, we find evidence for exponentially slow thermalization (in disorder) within the many-body localized regime when the rare region is present. We observe a decay of the spin imbalance in the bulk of the large disorder region that persists to long times $(\ensuremath{\sim}{10}^{4})$ and find a universal behavior of the spectral function.We numerically study quantum avalanches in one-dimensional disordered spin systems by attaching two XXZ spin chains. One chain has low disorder representing a rare Griffith's region, or thermal inclusion, and the second has larger disorder, i.e., disorder larger than the observed finite-size crossover. Comparing dynamics of this system to identical systems with uniformly large disorder, we find evidence for exponentially slow thermalization (in disorder) within the many-body localized regime when the rare region is present. We observe a decay of the spin imbalance in the bulk of the large disorder region that persists to long times $(\ensuremath{\sim}{10}^{4})$ and find a universal behavior of the spectral function.

arXiv:2303.02748Physical review. B./Physical review. BJul 18, 202320 citations

The Behavior of Many-Body Localization of Quasi-Disordered Spin-1/2 Chains

Jiali Zhang, Taotao Hu, Hang Ren +5 more

International Journal of Theoretical PhysicsApr 27, 20220 citations

Manifestations of Dynamical Localization in the Disordered XXZ Spin Chain

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