Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions

TL;DR

This paper uses the truncated Wigner approximation to study the relaxation dynamics of disordered interacting fermions in two dimensions, revealing faster semiclassical relaxation and a transient logarithmic relaxation linked to 1/f noise.

Contribution

It demonstrates the effectiveness of TWA in simulating large 2D disordered fermion systems and compares semiclassical and quantum relaxation behaviors.

Findings

Semiclassical dynamics relaxes faster than quantum dynamics.

Disordered 2D systems show transient logarithmic relaxation.

Logarithmic relaxation is associated with 1/f noise at strong disorder.

Abstract

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$-noise at strong disorder.