Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond

TL;DR

This paper explores the entanglement Hamiltonian of interacting lattice systems, demonstrating its local nature and relation to the model Hamiltonian with a spatially varying temperature, even in complex, non-symmetric systems.

Contribution

It shows that the entanglement Hamiltonian is approximately local and related to the model Hamiltonian with a smooth temperature profile, extending understanding beyond idealized models.

Findings

EH is practically local with dominant terms related to the model Hamiltonian.

Local temperature decays inversely with distance from the boundary.

Subdominant terms are suppressed away from the boundary.

Abstract

We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians. In this letter, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz symmetry, and (c) for subsystems with non-flat boundaries, up to relatively strong interactions. We show that the mentioned local temperature at a given point decays inversely proportional to its distance from the boundary between the subsystem and the environment. We find the subdominant terms in the EH as well and show that they are severely suppressed away from the boundaries of subsystem and are relatively small near them.