Momentum-space analysis of multipartite entanglement at quantum phase transitions

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.

8 pages, 4 figures

References in corpus (5)

• Quantum Phase Transitions and Bipartite Entanglement
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states