Impact of geometry on many-body localization

TL;DR

This paper investigates how the geometry of systems influences many-body localization, revealing that the transition to localization depends on the number of neighbors and can be modeled by the plasma model.

Contribution

It demonstrates the correlation between system geometry and the MBL transition, using exact diagonalization and energy level statistics.

Findings

Localization transition depends on number of neighbors

Plasma model describes the extended to localized crossover

Geometry influences ergodic to MBL phase transition

Abstract

The impact of geometry on many body localization is studied on simple, exemplary systems amenable to exact diagonalization treatment. The crossover between ergodic and MBL phase for uniform as well as quasi-random disorder is analyzed using statistics of energy levels. It is observed that the transition to many-body localized phase is correlated with the number of nearest coupled neighbors. The crossover from extended to localized systems is approximately described by the so called plasma model.