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arXiv:2108.08861 · SciPost Physics

Logarithmic, noise-induced dynamics in the Anderson insulator

Talía L. M. Lezama, Yevgeny Bar Lev

Published May 25, 2022• 23 citations
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Abstract

We study the dynamical behavior of the one-dimensional Anderson insulator in the presence of a local noise. We show that the noise induces logarithmically slow energy and entanglement growth, until the system reaches an infinite-temperature state, where both quantities saturate to extensive values. The saturation value of the entanglement entropy approaches the average entanglement entropy over all possible product states. At infinite temperature, we find that a density excitation spreads logarithmically with time, without any signs of asymptotic diffusive behavior. In addition, we provide a theoretical picture which qualitatively reproduces the phenomenology of particle transport.

DOI
10.21468/scipostphys.12.5.174

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We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer timescales, we show that the latter is a transient effect and that, eventually, the impurity spreads subdiffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a subdiffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator, and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasiperiodic potential.
We investigate how information spreads in three paradigmatic one-dimensional models with spatial disorder. The models we consider are unitarily related to a system of free fermions and, thus, are manifestly integrable. We demonstrate that out-of-time-order correlators can spread slowly beyond the single-particle localization length, despite the absence of many-body interactions. This phenomenon is shown to be due to the nonlocal relationship between elementary excitations and the physical degrees of freedom. We argue that this nonlocality becomes relevant for time-dependent correlation functions. In addition, a slow logarithmic-in-time growth of the entanglement entropy is observed following a quench from an unentangled initial state. We attribute this growth to the presence of strong zero modes, which gives rise to an exponential hierarchy of time scales upon ensemble averaging. Our work on disordered integrable systems complements the rich phenomenology of information spreading and we discuss broader implications for general systems with nonlocal correlations.
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The authors study the metal-insulator transition in the three-dimensional Anderson model from the entanglement perspective. They show that at the transition point the entanglement entropy after a quantum quench grows logarithmically in time, while the number entropy shows a double logarithmic growth. This behavior is consistent with exact bounds. It is also the same scaling recently found in many-body localized (MBL) phases, suggesting that the MBL phase might be more akin to an extended critical regime, rather than a fully localized phase.
When a group of compactly packed free fermions is allowed to spread over an empty one-dimensional lattice, the spreading particles can create entanglement between different parts of the lattice. We show, although breaking of translational invariance (TI) of the lattice by disorder slows down the spreading of local observables, the entanglement entropy of a subsystem can nonetheless receive a remarkable enhancement as long as the subsystem lies within the single-particle localization length. We show the main mechanism behind this enhancement is the reentrant exchange of particles between the subparts due to transport of mutual information due to backscattering. We discuss the length and timescales relevant to the phenomenon. We study the phenomenon for breaking of TI by both quasiperiodic and random potentials. We further explore the effect of randomness only in the initial state. This also exhibits a similar enhancement effect even in a TI lattice. We also touch upon the special case of periodic potential where qualitatively similar phenomenology emerges, although the coherence in the backscattering in this case leads to effects not captured by our simple yet generic picture.