The entanglement and relative entropy of a chiral fermion on the torus

Abstract

We derive the entanglement entropy of chiral fermions on the circle at arbitrary temperature. The spin-sector contribution depends only on the total length of the entangling region, regardless of the configuration of the intervals. Thus three-partite information provides a global indicator for the spin boundary conditions. Together with the modular Hamiltonian, our results provide a systematic way of obtaining relative entropy on the torus.

8 pages, 2 figures; corrected error in section C, some improvements to the exposition