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arXiv:2009.04501 · Physical review. E

Dynamical obstruction to localization in a disordered spin chain

Dries Sels, Anatoli Polkovnikov

Published Nov 8, 2021• 203 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.104.054105

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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.
Many-body localization(MBL) provides a mechanism by which isolated interacting quantum systems with disorder can avoid thermalization unlike ergodic systems satisfying the eigenstate thermalization hypothesis(ETH). Many-body localized systems retain signatures of their initial conditions at long times, whereas systems obeying ETH lose such information as they approach thermal equilibrium. Studying Non-equilibrium dynamics across ETH-MBL crossover is an important problem in condensed matter physics. Adiabatic control of parameters in interacting disordered systems provides a powerful framework to investigate MBL phases and their dynamical robustness. Using exact diagonalization and time-dependent numerical methods we study the effects of adiabatically ramped interactions in a disordered spin-1/2 XXZ chain, a paradigmatic model for exploring the many-body localization transition. By monitoring diagonal entropy density and entanglement entropy density growth across various ramp speeds, and system sizes. Our study incorporates Finite-size effects of spectral observables to probe the transition between ergodic and localized phases. The numerical results show that localized dynamical behavior remains largely intact under sufficiently slow ramp evolution, while increasing the driving rate promotes stronger excitation generation and larger entropy growth. This trend highlights the strong dependence of nonequilibrium adiabatic dynamics in disordered interacting quantum many-body systems.
We consider a one-dimensional spin chain system with quenched disorder and in the presence of a local periodic drive. We study the time evolution of the system in the Floquet basis and evaluate the fidelity susceptibility, which is a measure of how a given state changes under a small perturbation, of states to a weak periodic drive. We demonstrate that the statistical properties of the fidelity susceptibility over different disorder realizations can be used to identify two phases of the system: (1) the many-body localized phase, in which the susceptibility exhibits long tails while its average value decreases rapidly as disorder increases, and (2) the ergodic phase, in which the susceptibility distribution is narrow and its average value weakly depends on disorder. This distinction in the average value of the susceptibility between the two phases develops readily for systems with ten or more spins. Therefore, recently built networks of qubits subject to a local drive can simulate dynamics of a system in the many-body localization regime. We also show that the spin accumulation speed is correlated with the fidelity susceptibility and can also be used to distinguish the two phases.
The disordered XXZ model is a prototype model of the many-body localization (MBL) transition. Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due to severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.
The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.
We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain.We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian.The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case.At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit.We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase.We propose a criterion to identify the position of the transition by looking at the long tails of these distributions.The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.
We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one-dimensional (1D) random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a nonextensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.