Investigating disordered many-body system with entanglement in momentum space

TL;DR

This paper explores how entanglement in momentum space reveals localization and phase transition phenomena in a disordered one-dimensional fermion system with attractive interactions, offering new insights into many-body localization.

Contribution

It introduces a novel entanglement spectrum analysis to identify localization and phase transitions in a disordered fermion model, highlighting the role of paired-fermion entanglement.

Findings

Identification of two components in the entanglement spectrum related to fermion pairing.

Localization transition indicated by the vanishing of a component in the entanglement spectrum.

Phase transition induced by interaction is unaffected by disorder.

Abstract

We study the entanglement in momentum space of the ground state of a disordered one-dimensional fermion lattice model with attractive interaction. We observe two components in the entanglement spectrum, one of which is related to paired-fermion entanglement and contributes to the long-range correlation in position space. The vanishing point of it indicates the localization phenomenon in the ground state of this model. Additionally, by method of entanglement spectrum, we provide a new evidence to show the transition of two phases induced by interaction, and fnd that this phase transition is not infuenced by the disorder. Our result show key characteristics in entanglement for different phases in the system, and provide a novel perspective to understand localization phenomena.