Entanglement Entropy for Disjoint Subsystems in XX Spin Chain

Abstract: Fisher-Hartwig formula has been successful applied to describe the von Neumann and R\'enyi entropies of a block of spins in the ground state of XX spin chain. It was based on a determinant representation. In this paper, we generalize the free fermion method to obtain an exact formulation for the entropy of any finite subsystem in XX spin chain. Based on this, we derive a determinant representation of the entropy of multiple disjoint intervals in the ground state of $XX$ model.