Resonant energy scales and local observables in the many-body localised phase

TL;DR

This paper develops a theoretical framework for understanding resonances in the many-body localized phase of disordered quantum spin chains, revealing universal correlations and power-law distributions of energy scales and local observables.

Contribution

It introduces a novel theory linking local observable matrix elements to energy scales in MBL, with analytical and numerical validation of resonance distributions.

Findings

Resonance energies follow a power-law distribution.

Local observables show universal correlations with the spectrum.

Eigenstate sensitivities to local perturbations are characterized.

Abstract

We formulate a theory for resonances in the many-body localised (MBL) phase of disordered quantum spin chains in terms of local observables. A key result is to show that there are universal correlations between the matrix elements of local observables and the many-body level spectrum. This reveals how the matrix elements encode the energy scales associated with resonance, thereby allowing us to show that these energies are power-law distributed. Using these results we calculate analytically the distributions of local polarisations and of eigenstate fidelity susceptibilities. The first of these quantities characterises the proximity of MBL systems to noninteracting ones, while the second highlights their extreme sensitivity to local perturbations. Our theoretical approach is to consider the effect of varying a local field, which induces a parametric dynamics of spectral properties. We corroborate our results numerically using exact diagonalisation in finite systems.