Concurrence distribution in excited states of the one-dimensional spin-1/2 transverse-field XY model: Two different regions.

Abstract

We investigate the variation of concurrence in a spin-1/2 transverse field XY chain system in an excited state. Initially, we precisely solve the eigenvalue problem of the system Hamiltonian using the fermionization technique. Subsequently, we calculate the concurrence between nearest-neighbor pairs of spins in all excited states with higher energy than the ground state. Below the factorized field, denoted as h_{f}=sqrt[J^{2}-(Jδ)^{2}], we find no pairwise entanglement between nearest neighbors in excited states. At the factorized field, corresponding to a factorized state, we observe weak concurrence in very low energy states. Beyond h_{f}, the concurrence strengthens, entangling all excited states. The density of entangled states peaks at the center of the excited spectrum. Additionally, the distribution of concurrence reveals that the midpoint of the nonzero concurrence range harbors the most entangled excited states.