Time Evolution of Many-Body Localized Systems with the Flow Equation Approach

TL;DR

This paper introduces a semi-analytical flow equation method to study the time evolution of many-body localized systems, providing new insights into local integrals of motion and dynamics in both one and two dimensions.

Contribution

The paper develops a novel flow equation approach to analyze many-body localization, explicitly constructing local integrals of motion and exploring dynamics in higher dimensions.

Findings

Constructed local integrals of motion in 1D MBL systems.

Calculated local integrals of motion in 2D for the first time.

Revealed the role of l-bit interactions in dephasing and relaxation.

Abstract

The interplay between interactions and quenched disorder can result in rich dynamical quantum phenomena far from equilibrium, particularly when many-body localization prevents the system from full thermalization. With the aim of tackling this interesting regime, here we develop a semi-analytical flow equation approach to study time evolution of strongly disordered interacting quantum systems. We apply this technique to a prototype model of interacting spinless fermions in a random on-site potential in both one and two dimensions. Key results include (i) an explicit construction of the local integrals of motion that characterize the many-body localized phase in one dimension, ultimately connecting the microscopic model to phenomenological descriptions, (ii) calculation of these quantities for the first time in two dimensions, and (iii) an investigation of the real-time dynamics in the localized phase which reveals the crucial role of $l$-bit interactions for enhancing dephasing and relaxation.