Phenomenology of spectral functions in disordered spin chains at infinite temperature

TL;DR

This paper develops a phenomenological theory to explain spectral function features in disordered spin chains at infinite temperature, linking dynamics to proximity to Anderson insulator behavior and local integrals of motion.

Contribution

It introduces a theory connecting spectral properties of disordered spin chains to Anderson localization and local integrals of motion, providing quantitative descriptions across disorder strengths.

Findings

Quantitative match with spectral functions in disordered systems.

Proximity to Anderson insulator influences observable dynamics.

Theory applies across a wide disorder range.

Abstract

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.