Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains

TL;DR

This paper explores how nonabelian SU(2) symmetry in disordered isotropic Heisenberg spin chains affects many-body localization, revealing a transition to an incomplete localization phase through numerical analysis.

Contribution

It provides numerical evidence that nonabelian symmetry hinders full many-body localization, showing a crossover rather than a sharp transition in exchange-disordered spin chains.

Findings

Transition from ergodic to incompletely localized phase

Sample-to-sample variance peaks at the transition

Incomplete localization distinguished by variance scaling

Abstract

We investigate many-body localization in isotropic Heisenberg spin chains with the local exchange parameters being subject to quenched disorder. Such systems incorporate a nonabelian symmetry in their Hamiltonian by an invariance under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the emergence of a many-body localized phase even in presence of strong disorder. We report on numerical studies using exact diagonalization for chains of common spin length 1/2 and 1. The averaged consecutive-gap ratios display a transition compatible with a crossover from an ergodic phase at small disorder strength to an incompletely localized phase at stronger disorder. The sample-to-sample variance of the averaged consecutive-gap ratio displays a maximum at the transition and distinguishes the incompletely localized phase from a fully many-body localized phase by its scaling behavior.