Universal semiclassical dynamics in disordered two-dimensional systems

TL;DR

This paper introduces a single-trajectory fermionic truncated Wigner approximation that accurately models the dynamics of disordered 1D and 2D fermionic systems, revealing universal behavior in imbalance decay.

Contribution

The study demonstrates that a simplified fermionic truncated Wigner approximation effectively captures 2D disordered system dynamics and uncovers universal temporal scaling.

Findings

The imbalance shows universal dependence on rescaled time t/ξ_W in both 1D and 2D.

In 2D, the time-scale ξ_W depends on disorder strength via a stretched-exponential.

The method enables studying larger 2D systems than standard approaches.

Abstract

The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/\xi_W$, where in 2D the time-scale $\xi_W$ follows a stretched-exponential dependence on disorder strength.