# Entanglement of a chiral fermion on the torus

## TL;DR

This paper derives a new modular Hamiltonian for a chiral fermion on a circle at finite temperature, providing explicit formulas for multiple intervals and a simplified entanglement entropy expression.

## Contribution

It introduces a detailed calculation of the modular Hamiltonian for a chiral fermion on a torus, extending existing results to arbitrary intervals and finite temperature.

## Key findings

- Explicit modular Hamiltonian for multiple intervals
- Simplified expression for entanglement entropy
- Validation against known limits and computations of modular flow

## Abstract

In this paper we present the detailed calculation of a new modular Hamiltonian, namely that of a chiral fermion on a circle at non-zero temperature. We provide explicit results for an arbitrary collection of intervals, which we discuss at length by checking against known results in different limits and by computing the associated modular flow. We also compute the entanglement entropy, and we obtain a simple expression for it which appears to be more manageable than those already existing in the literature.