Phase transition of a heavy-fermion superconductor in a high magnetic field: Entanglement analysis

Abstract

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 CeCoIn5 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.