Memory effects in the density-wave imbalance in delocalized disordered systems

TL;DR

This paper studies how memory effects influence the long-time decay of the density-wave imbalance in disordered many-body systems, revealing a power-law decay linked to transport properties and dimensionality.

Contribution

It provides analytical and numerical insights into the role of memory effects in the imbalance dynamics of disordered systems across different dimensions.

Findings

Imbalance decays as a power law due to memory effects.

Decay exponent depends on transport law and dimensionality.

Numerical simulations support analytical predictions.

Abstract

Dynamics of the imbalance in occupations on even and odd sites of a lattice serves as one of the key characteristics for identification of the many-body localization transition. In this work, we investigate the long-time behaviour of the imbalance in disordered one- and two-dimensional many-body systems in the regime of diffusive or subdiffusive transport. We show that memory effects originating from a coupling between slow and fast modes lead to a power-law decay of the imbalance, with the exponent determined by the diffusive (or subdiffusive) transport law and the spatial dimensionality. Analytical results are supported by numerical simulations performed on a two-dimensional system in the regime of weak localization.