Entanglement in extended Hubbard models and quantum phase transitions

TL;DR

This paper investigates how bipartite and multipartite entanglement behave at quantum phase transitions in an exactly solvable extended Hubbard model, revealing divergence of entanglement range and introducing a correlation ratio to analyze quantum correlations.

Contribution

It provides a detailed analysis of entanglement properties at QPTs in a 1D extended Hubbard model, including the introduction of the correlation ratio for qudit systems.

Findings

Entanglement range diverges at transition points.

Correlation ratio captures the role of quantum correlations.

Finite mutual information indicates off-diagonal long-range order.

Abstract

The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correlated electron systems is investigated. We consider a bond-charge extended Hubbard model exactly solvable in one dimension which displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees of freedom involved. The analysis is carried out by means of appropriate measures of bipartite/multipartite quantum correlations. It is found that all transitions ascribed to two-point correlations are characterized by an entanglement range which diverges at the transition points. The exponent coincides with that of the correlation length at the transitions. We introduce the correlation ratio, namely, the ratio of quantum mutual information and single-site entanglement. We show that at T=0, it captures the relative role of two-point and multipartite quantum correlations at transition points, generalizing to qudit systems the entanglement ratio. Moreover, a finite value of quantum mutual information between infinitely distant sites is seen to quantify the presence of off-diagonal long-range order induced by multipartite entanglement.