Properties of the entanglement Hamiltonian for finite free-fermion chains

TL;DR

This paper investigates the properties of the entanglement Hamiltonian in finite free-fermion chains, revealing spectral and eigenfunction characteristics, and extending findings to the critical transverse Ising model.

Contribution

It provides a detailed analysis of the entanglement Hamiltonian's spectral properties and commutation relations in free-fermion chains and their extension to the transverse Ising model.

Findings

Single-particle spectra and eigenfunctions characterized

Scaling relation between eigenvalues established

Commutation properties extended to the transverse Ising model

Abstract

We study the entanglement Hamiltonian for fermionic hopping models on rings and open chains and determine single-particle spectra, eigenfunctions and the form in real space. For the chain, we find a commuting operator as for the ring and compare with its properties in both cases. In particular, a scaling relation between the eigenvalues is found for large systems. We also show how the commutation property carries over to the critical transverse Ising model.