Local resonances and parametric level dynamics in the many-body localised phase

TL;DR

This paper investigates how local resonances influence spectral properties in the many-body localized phase by analyzing parametric level dynamics and developing a resonance theory based on local integrals of motion.

Contribution

It introduces a parametric approach to describe resonances in the MBL phase, linking level crossings to LIOM configurations and analyzing their impact on spectral statistics.

Findings

Resonances cause avoided level crossings in the MBL phase.

Large level curvatures are associated with resonances.

Distributions of local observable matrix elements are characterized.

Abstract

By varying the disorder realisation in the many-body localised (MBL) phase, we investigate the influence of resonances on spectral properties. The standard theory of the MBL phase is based on the existence of local integrals of motion (LIOM), and eigenstates of the time evolution operator can be described as LIOM configurations. We show that smooth variations of the disorder give rise to avoided level crossings, and we identify these with resonances between LIOM configurations. Through this parametric approach, we develop a theory for resonances in terms of standard properties of non-resonant LIOM. This framework describes resonances that are locally pairwise, and is appropriate in arbitrarily large systems deep within the MBL phase. We show that resonances are associated with large level curvatures on paths through the ensemble of disorder realisations, and we determine the curvature distribution. By considering the level repulsion associated with resonances we calculate the two-point correlator of the level density. We also find the distributions of matrix elements of local observables and discuss implications for low-frequency dynamics.