Many body localization in the presence of a single particle mobility edge

TL;DR

This paper investigates how interactions affect many-body localization in one-dimensional quasiperiodic systems with single-particle mobility edges, revealing MBL in one model with atypical entanglement growth.

Contribution

It demonstrates the occurrence of many-body localization in models with mobility edges and analyzes the unique entanglement dynamics in such systems.

Findings

MBL occurs in one of the studied models with mobility edges

Entanglement entropy grows faster than logarithmically in time

Level spacing and conductivity indicate localization transition

Abstract

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.