Momentum-space analysis of multipartite entanglement at quantum phase transitions

Julia Stasińska, Benjamin Rogers, Mauro Paternostro +2 more

Josep Amengual i Batle, Majid Alkhambashi, Ahmed Farouk +2 more

Pedro Ribeiro, Yasser Omar, Vitor Rocha Vieira

Alberto Anfossi, Paolo Giorda, Arianna Montorsi

We investigate entanglement properties at quantum phase transitions (QPTs) of a one-dimensional 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 $\ensuremath{\eta}$-pairing mechanism). We first detect the two or multipartite 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 quantum correlations in the momentum representation and the relevant (superconducting) ones exhibited in the complementary picture: the direct-lattice representation. We then investigate the presence of multipartite entanglement in momentum space by means of a generalization of the Meyer-Wallach measure and we relate its behavior to the nature of the various QPTs.

R. Afzali, N. Ebrahimian

When the magnetic field is only acting on the spin of electrons, a transition from a normal to a modulated superconducting state or Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state may occur at low temperatures. A FFLO superconducting state, which accompanies an order parameter that oscillates spatially, may be stabilized by a high applied magnetic field or a molecular field. Quantum multipartite entanglement is a new procedure for investigating quantum phase transitions. In this article, we deal with the phase transition of the FFLO state of CeCoIn 5 to a normal state by obtaining quantum multipartite entanglement of the system. For this purpose, using normal and anomalous Green functions and the density matrix, we obtain concurrence, as a measure of bipartite entanglement. Then, the order parameter and the magnetic -field dependence of multipartite entanglement in momentum space is calculated. The phase transition is determined, and the behavior of the system based on order parameter is discussed. Furthermore, the phase transitions of both the Bardeen-Cooper-Schrieffer (BCS) and FFLO states to the normal state are compared.

Hai‐Qing Lin, Shi-Jian Gu, Guang-Shan Tian