Discrete disorder models for many-body localization

TL;DR

This paper investigates many-body localization in a 1D Heisenberg chain using exact diagonalization, comparing discrete and continuous disorder models, and finds that most discrete distributions yield similar results to continuous ones after rescaling, except for binary distributions.

Contribution

It introduces and compares various discrete disorder models in many-body localization, showing their equivalence to continuous models after rescaling, with notable deviations for binary distributions.

Findings

Discrete disorder models largely replicate continuous distribution results after rescaling.

Binary distribution shows significant deviations from other models.

Energy level statistics and non-ergodic behavior are consistent across models after rescaling.

Abstract

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time non-ergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.