# Relaxation mechanisms in a disordered system with the Poisson level statistics

## TL;DR

This paper investigates how disorder and spin symmetry influence localization in a disordered anisotropic t-J model, revealing that symmetry-preserving disorder allows localization within sectors but enables certain operators to relax due to symmetry sector mixing.

## Contribution

It demonstrates that in the anisotropic t-J model, localization persists within symmetry sectors under symmetry-preserving disorder, while symmetry-breaking disorder leads to full localization, highlighting the role of symmetry in many-body localization.

## Key findings

- Localization occurs within each symmetry sector for symmetry-preserving disorder.
- Odd operators relax due to transitions between symmetry sectors.
- Level statistics suggest localization within sectors despite operator relaxation.

## Abstract

We discuss the interplay between many-body localization and spin-symmetry. To this end, we study the time evolution of several observables in the anisotropic t-J model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom, yet it has smaller Hilbert space and thus allows for numerical studies of larger systems. We compare the field disorder that breaks the Z_2 spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the Z_2 spin transformation relax towards the equilibrium value at relatively short time scales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry preserving disorder. Odd operators' apparent relaxation is due to their time evolution between distinct symmetry sectors.