Entanglement properties and quantum phases for a fermionic disordered one dimensional wire with attractive interactions

TL;DR

This paper investigates how entanglement entropy and spectrum can distinguish between localized, metallic, and superconducting phases in a disordered one-dimensional fermionic wire with attractive interactions, revealing unique entanglement signatures.

Contribution

It demonstrates that entanglement properties can uniquely identify different quantum phases in disordered fermionic systems, providing new diagnostic tools.

Findings

Superconducting phase shows a Levy alpha stable distribution of entanglement entropy.

Entanglement level spacing distribution is unitary in the superconducting phase.

Entanglement properties reveal phase distinctions not detectable by other methods.

Abstract

A fermionic disordered one dimensional wire in the presence of attractive interactions is known to have two distinct phases: A localized and a superconducting one depending on the strength of interaction and disorder. The localized region may also exhibit a metallic behaviour if the system size is shorter than the localization length. Here we show that the superconducting phase has a distinct distribution of the entanglement entropy and entanglement spectrum distinct from the metallic regime. The entanglement entropy distribution is strongly asymmetric with L\'evy alpha stable distribution (compared to the Gaussian metallic distribution), and the entanglement level spacing distribution is unitary (compared to orthogonal). Thus, entanglement properties may reveal properties which can not be detected by other methods.