Energy diffusion in the ergodic phase of a many body localizable spin chain

Varma, Vipin Kerala; Lerose, Alessio; Pietracaprina, Francesca; Goold, John; Scardicchio, Antonello

doi:10.1088/1742-5468/aa668b

Cited by 48 publications

(57 citation statements)

References 52 publications

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“…[58], provided the interpretation of these results in terms of Griffiths physics. These numerical studies, as well as subsequent work using exact diagonalization [89,90], and approximate memory-matrix approaches [91] found anomalous diffusion at essentially all values of disorder. (In Ref.…”

Section: Numerical Evidencementioning

confidence: 76%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

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Section: Numerical Evidencementioning

confidence: 76%

Rare‐region effects and dynamics near the many‐body localization transition

et al. 2017

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“…Generic arguments and numerical evidence on very small systems (about 20 spins) have been put forward for the existence of subdiffusive transport of spin [17][18][19][20] and energy [18,21,22]. A number of recent works have analyzed its spin transport properties in the ergodic phase, finding different results.…”

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confidence: 99%

Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System

2016

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We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.Introduction.-There are ever increasing technological capabilities in simulating isolated quantum systems through cold atomic gases [1] and, recently, through coupled, controlled superconducting qubits [2]. While there is a commensurately good theoretical handle on capturing ground state properties of such systems [3], understanding their dynamical properties, especially away from the ground state, is fraught with analytical and numerical challenges.Despite this, in the recent years we have witnessed a change in paradigm in the study of isolated quantum systems, in particular with regard to the role that disorder plays in such systems. The turning point came about from the study of Anderson localization [4] in interacting, many-body quantum systems [5]. The observation that disorder and quantum effects can hinder transport (of energy, charge or spin) even at an infinite temperature and in the presence of interactions [6] opened the door to a new phenomenology of a so-called manybody localized (MBL) phase exhibiting many unique and interesting properties. Slow growth of entanglement [7,8], emergent integrability [9], protection of symmetries [10], and change in the properties of eigenstates [11][12][13] are a few of the peculiar properties of this newly identified phase; see review [14] for a comprehensive list. The implications of the new MBL physics, being inherently robust, are far reaching, going from fundamental physics to the theory of quantum computation [15], some of which have already been experimentally probed [16].While the deep MBL region (in one dimensional systems) is well understood, much remains to be said about the conducting regime and the transition to it. Although both aspects are important, here we focus on characterizing the conducting phase, in particular its transport properties, in, what is by now, an archetypal model that harbors the MBL phase, i.e., the one dimensional anisotropic Heisenberg model.Generic arguments and numerical evidence on very small systems (about 20 spins) have been put forward for the existence of subdiffusive transport of spin [17][18][19][20] and energy [18,21,22]. A number of recent works have analyzed its sp...

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“…In contrast, the spreading of information in noninteracting Anderson insulators is completely frozen [32,33]. The ergodic phase of this model, occurring for W < W c , exhibits anomalous subdiffusive spin transport characterized by a dynamical exponent varying continuously with disorder strength [34][35][36][37][38][39][40][41][42][43][44], but also a sublinear EE growth [36] (cf. Ref.…”

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confidence: 99%

Information propagation in isolated quantum systems

2017

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Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time-evolution we show that for weakly disordered nonintegrable systems information propagates behind a ballistically moving front, and the entanglement entropy growths linearly in time. For stronger disorder the motion of the information front is algebraic and sub-ballistic and is characterized by an exponent which depends on the strength of the disorder, similarly to the sublinear growth of the entanglement entropy. We show that the dynamical exponent associated with the information front coincides with the exponent of the growth of the entanglement entropy for both weak and strong disorder. We also demonstrate that the temporal dependence of the OTOC is characterized by a fast nonexponential growth, followed by a slow saturation after the passage of the information front. Finally,we discuss the implications of this behavioral change on the growth of the entanglement entropy.Introduction. -While the speed of light is the absolute upper limit of information propagation in both classical and quantum relativistic systems, surprisingly a velocity which plays a similar role exists also for shortrange interacting nonrelativistic quantum systems. This velocity, known as the Lieb-Robinson velocity, bounds the spreading of correlations in the system and implies that information about local initial excitations propagates within a causal "light-cone", similarly to the lightcone encountered in the theory of special relativity [1]. The shape of the light-cone can be obtained from the correlation function

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Energy diffusion in the ergodic phase of a many body localizable spin chain

Cited by 48 publications

References 52 publications

Rare‐region effects and dynamics near the many‐body localization transition

Rare‐region effects and dynamics near the many‐body localization transition

Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System

Information propagation in isolated quantum systems

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