Momentum-space analysis of multipartite entanglement at quantum phase transitions

TL;DR

This paper analyzes multipartite entanglement at quantum phase transitions in an extended Hubbard model using momentum space representation, revealing the nature of correlations and their relation to phase transitions.

Contribution

It introduces a momentum space approach to study multipartite entanglement at quantum phase transitions, utilizing the Q-measure for detailed correlation analysis.

Findings

Multipartite entanglement increases at quantum phase transitions.

Momentum space correlations relate to lattice representation.

The Q-measure effectively captures entanglement sensitivity.

Abstract

We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of modes (electrons coupled through the eta-pairing mechanism). We first detect the two/multi-partite nature of each quantum phase transition by a comparative study of the singularities of Von Neumann entropy and quantum mutual information. We establish the existing relations between the correlations in the momentum representation and those exhibited in the complementary picture: the direct lattice representation. The presence of multipartite entanglement is then investigated in detail through the Q-measure, namely a generalization of the Meyer-Wallach measure of entanglement. Such a measure becomes increasingly sensitive to correlations of a multipartite nature increasing the size of the reduced density matrix. In momentum space, we succeed in obtaining the latter for our system at arbitrary size and we relate its behaviour to the nature of the various QPTs.