Thouless Energy Across Many-Body Localization Transition in Floquet Systems

TL;DR

This paper studies how the Thouless energy scales across the many-body localization transition in Floquet systems, using multiple methods to provide a comprehensive understanding of the transition point and its characteristics.

Contribution

It establishes a connection between different definitions of Thouless energy in many-body systems and offers new insights into the MBL transition in Floquet models.

Findings

Thouless energy remains system-size independent in the ergodic phase.

At the transition, Thouless energy becomes comparable to level spacing.

Consistent estimates of the transition point are obtained across different probes.

Abstract

The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g. typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, the Thouless energy tends to a value independent of system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of the Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting, and yields new insights into the MBL transition in Floquet systems.