On the relation between entanglement and subsystem Hamiltonians

TL;DR

This paper explores the conditions under which the entanglement Hamiltonian is proportional to the subsystem Hamiltonian, especially near maximal entanglement, and examines how this relationship changes in solvable models away from that limit.

Contribution

It identifies specific conditions for the proportionality between entanglement and subsystem Hamiltonians and analyzes how the coupling range differs in solvable models away from maximal entanglement.

Findings

Proportionality holds near maximal entanglement under certain conditions.

Coupling range differs between entanglement and subsystem Hamiltonians away from the limit.

Solvable models illustrate the change in relationship away from maximal entanglement.

Abstract

We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling range differs in both quantities and allow to investigate the effect.