Logarithmic, noise-induced dynamics in the Anderson insulator

TL;DR

This paper investigates how local noise affects the dynamics of the Anderson insulator, revealing logarithmically slow growth of energy and entanglement, leading to saturation at infinite temperature, with implications for understanding particle transport.

Contribution

It introduces a theoretical framework explaining noise-induced logarithmic dynamics in the Anderson insulator, highlighting the transition to infinite-temperature saturation.

Findings

Energy and entanglement grow logarithmically over time

Saturation of entanglement entropy approaches average over all product states

Density excitation spreads logarithmically without diffusive behavior

Abstract

We study the dynamical behavior of the 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.