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arXiv:1810.01593 · Physical review. B./Physical review. B

Transient and persistent particle subdiffusion in a disordered chain coupled to bosons

Peter Prelovšek, J. Bonča, Marcin Mierzejewski

Published Sep 10, 2018• 17 citations
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Abstract

We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between dynamics due to noninteracting bosons and hard-core bosons. In the first case the transient dynamics is subdiffusive, but multiboson processes allow for long-time normal diffusion, while hard-core effects suppress multiboson processes leading to persistent subdiffusive transport, consistent with numerical results for a full many-body evolution. In contrast, analogous study for a quasiperiodic potential reveals a stable long-time diffusion.

DOI
10.1103/physrevb.98.125119

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We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between dynamics due to noninteracting bosons and hard-core bosons. In the first case the transient dynamics is subdiffusive, but multiboson processes allow for long-time normal diffusion, while hard-core effects suppress multiboson processes leading to persistent subdiffusive transport, consistent with numerical results for a full many-body evolution. In contrast, analogous study for a quasiperiodic potential reveals a stable long-time diffusion.
We study a quantum particle coupled to hard-core bosons and propagating on disordered ladders with RRR legs, ranging from R=1R=1R=1 (chains) to $R\ensuremath{\gg}1$ (planes). The particle dynamics is studied within the framework of rate equations for the boson-assisted transitions between the Anderson states. We demonstrate that for finite $R<\ensuremath{\infty}$ and sufficiently strong disorder the dynamics is nondiffusive, while two-dimensional planar systems with $R\ensuremath{\rightarrow}\ensuremath{\infty}$ remain diffusive for arbitrarily strong disorder. The transition from diffusive to subdiffusive regimes may be identified via statistical fluctuations of resistivity. Close to the transition, the corresponding distribution function in the diffusive regime has fat tails which decrease much slower than 1/L1/\sqrt{L}1/L​, where LLL is the system size. Finally, we present evidence that similar non-Gaussian fluctuations arise also in standard models of many-body localization.
A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual time-dependent drift velocity, which appears as a consequence of a constant electric field. We show that GER remains valid much beyond the regime of the linear response. Qualitatively, it holds true up to strongest drivings when the nonlinear field effects lead to the Stark-like localization. Numerical calculations based on full quantum evolution are substantiated by much simpler rate equations for the boson-assisted transitions between localized Anderson states.
We study a particle which propagates in a one-dimensional strong random potential and is coupled to a bosonic bath. We independently test various properties of bosons (hopping term, hard-core effects, and generic boson-boson interaction) and show that bosonic itineracy is the essential ingredient governing the dynamics of the particle. Coupling of the particle to itinerant phonons or hard-core bosons alike leads to delocalization of the particle by virtue of a subdiffusive (or diffusive) spread from the initially localized state. Delocalization remains in effect even when the boson frequency and the bandwidth of itinerant bosons remain an order of magnitude smaller than the magnitude of the random potential. When the particle is coupled to localized bosons, its spread remains logarithmic or even sublogarithmic. The latter result together with the survival probability shows that the particle remains localized despite being coupled to bosons.
We study high-temperature magnetization transport in a many-body spin-1/2 chain with on-site quasiperiodic potential governed by the Fibonacci rule. In the absence of interactions it is known that the system is critical with the transport described by a continuously varying dynamical exponent (from ballistic to localized) as a function of the on-site potential strength. Upon introducing weak interactions, we find that an anomalous noninteracting dynamical exponent becomes diffusive for any potential strength. This is borne out by a boundary-driven Lindblad dynamics as well as unitary dynamics, with agreeing diffusion constants. This must be contrasted to a random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small UUU always slows down the noninteracting dynamics to subdiffusion, and is therefore unable to describe diffusion in an interacting quasiperiodic system. Finally, briefly exploring larger interactions we find a regime of interaction-induced subdiffusive dynamics, despite the on-site potential itself having no ``rare regions.''
We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a parametrically large intermediate-time window. We argue for this intermediate-time subdiffusive regime both analytically and using numerical simulations on single-particle localized systems. Furthermore, we show that normal diffusion is restored in the long-time limit, through processes analogous to variable-range hopping. With numerical simulations based on Lanczos exact diagonalization, we demonstrate that our qualitative conclusions are also valid for interacting systems in the many-body localized phase.
We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By studying eigenstates of the full Hamiltonian, for strong disorders we find that the dynamics is confined up to very long times to disconnected MB clusters in the Fock space. By keeping only resonant contributions and simplifying the quantum problem to rate equations (REs) for MB states, in analogy with percolation problems, the MBL transition is located via the universal cluster distribution and the emergence of the macroscopic cluster. On the ergodic side, our approximate RE approach to the relaxation processes captures well the diffusion transport, as found for the full quantum model. In a broad transient regime, we find an anomalous, i.e., subdiffusivelike, transport, emerging from weak links between MB states.