Effect of long-range hopping and interactions on entanglement dynamics and many-body localization

TL;DR

This paper explores how long-range hopping and interactions influence entanglement growth and many-body localization in a disordered chain of spinless fermions, revealing unique scaling behaviors and an analogy to higher-dimensional systems.

Contribution

It introduces a numerical study of entanglement dynamics in long-range disordered fermionic chains, highlighting novel scaling laws and an analogy to higher-dimensional MBL physics.

Findings

Entanglement entropy scales as ln t in certain regimes.

Saturation entanglement scales as ln L with system size.

Long-range hopping affects the MBL transition and entanglement growth.

Abstract

We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalization-localization transition with increasing disorder. We find an interesting regime in this noninteracting disordered chain where the long-time entanglement entropy scales as $S(t) \sim \ln t$ and the saturated entanglement entropy scales with system size $L$ as $S(L,t \to {\infty}) \sim \ln L$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.