Entanglement Hamiltonians for non-critical quantum chains

TL;DR

This paper investigates the structure of entanglement Hamiltonians in non-critical quantum chains, revealing how their profiles and couplings evolve near criticality through high-precision numerical analysis of free-particle models.

Contribution

It provides a detailed numerical and analytical study of entanglement Hamiltonians in non-critical free-particle quantum chains, highlighting the transition from simple to complex coupling profiles near criticality.

Findings

Triangular profiles of dominant terms far from criticality

Longer-range couplings become significant near criticality

Exact spectra and entanglement entropies closely match dominant Hamiltonian terms

Abstract

We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.