Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge

TL;DR

This paper investigates many-body localization in a quasiperiodic model with long-range hopping and a mobility edge, revealing different phases and the impact of interactions on localization behavior.

Contribution

It introduces a detailed phase diagram of the $t_1$-$t_2$ model, highlighting the role of NNN hopping and interactions in many-body localization phenomena.

Findings

Weak interactions lead to nonthermal phases.

Intermediate interactions show behavior similar to the Aubry-Andre model.

Strong interactions reveal new physics due to NNN hopping breaking Hilbert space fragmentation.

Abstract

We study many-body localization (MBL) in the quasiperiodic $t_1$-$t_2$ model, focusing on the role of next-nearest-neighbor (NNN) hopping $t_2$, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction $U$. For weak interactions ($U\ll t_1$), this model is always nonthermal. For intermediate interactions ($U\sim t_1$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\gg t_1)$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.