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

## TL;DR

This paper derives the entanglement entropy of chiral fermions on a torus at any temperature, revealing how spin-sector contributions depend solely on the total length of the entangling region and offering insights into relative entropy and boundary conditions.

## Contribution

It provides a systematic derivation of entanglement entropy for chiral fermions on a torus, highlighting the role of spin sectors and boundary conditions.

## Key findings

- Spin-sector contribution depends only on total entangling region length.
- Three-partite information indicates global spin boundary conditions.
- Method enables systematic calculation of relative entropy 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.