Local integrals of motion in the two-site Anderson-Hubbard model

TL;DR

This paper investigates the explicit form and localization properties of pseudospins in a disordered two-site Hubbard model, shedding light on the structure of local integrals of motion in minimal many-body localized systems.

Contribution

It provides a detailed analysis of the optimal local pseudospins in a two-site disordered Hubbard model, highlighting their evolution with system parameters.

Findings

Optimal pseudospins become less localized as hopping increases.

Distribution of non-optimal pseudospins is broad and varies with system parameters.

Explicit pseudospin forms reveal insights into many-body localization in minimal systems.

Abstract

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. Due to the multitude of ways to define these, the explicit identification of the optimally local pseudospins in specific systems is non-trivial. Given continuing intense interest in the role of disorder in strongly correlated systems, we consider the disordered Hubbard model. Focusing on a two-site system, we track the evolution of the optimally localized pseudospins as hopping and interactions are varied to move the system away from the trivially localized atomic limit, examining the explicit form of the pseudospins and exploring the broad distribution of non-optimal forms.