Two-Point Versus Multipartite Entanglement in Quantum Phase Transitions

TL;DR

This paper investigates how different types of quantum correlations, specifically two-point versus multipartite entanglement, relate to quantum phase transitions in an exactly solvable one-dimensional extended Hubbard model.

Contribution

It introduces a method to distinguish the roles of bipartite and shared quantum correlations in quantum phase transitions using entanglement measures and mutual information.

Findings

Single-site entanglement reproduces the phase diagram.

Comparison of entanglement and mutual information reveals the nature of correlations.

Negativity serves as a benchmark for bipartite entanglement at transitions.

Abstract

We analyze correlations between subsystems for an extended Hubbard model exactly solvable in one dimension, which exhibits a rich structure of quantum phase transitions (QPTs). The T=0 phase diagram is exactly reproduced by studying singularities of single-site entanglement. It is shown how comparison of the latter quantity and quantum mutual information allows one to recognize whether two-point or shared quantum correlations are responsible for each of the occurring QPTs. The method works in principle for any number D of degrees of freedom per site. As a by-product, we are providing a benchmark for direct measures of bipartite entanglement; in particular, here we discuss the role of negativity at the transition.