Modular Hamiltonian and entanglement entropy in the BMS free fermion theory

TL;DR

This paper analyzes the modular Hamiltonian and entanglement entropy in the BMS-invariant free fermion model, revealing local and bi-local structures and providing explicit calculations for multiple disjoint intervals.

Contribution

It introduces a method to compute the modular Hamiltonian for multiple disjoint intervals in the BMS free fermion theory, combining geometric and background field techniques.

Findings

Modular Hamiltonian includes local and bi-local terms.

Derived a relation between Wightman functions and the modular Hamiltonian.

Computed entanglement entropy for multiple disjoint intervals.

Abstract

We study the modular Hamiltonian and the entanglement entropy of the BMS-invariant free fermion model. Starting from the modular Hamiltonian on a half-line interval, we calculate the modular Hamiltonian for a region consisting of two disjoint intervals using the uniformization map and a background field method. The resulting modular Hamiltonian contains a local term which generates a geometrical flow, and a bi-local term which mixes operators between the two intervals. We further derive a relation between Wightman functions and the modular Hamiltonian using both diagonalization and a coherent state method. This enables us to compute the entanglement entropy for multi-disjoint intervals. Our explicit results in the BMS free fermion model are compatible with earlier ones based on symmetry and holography.