Entanglement Thermodynamics

TL;DR

This paper explores the connection between entanglement spectra and thermodynamics, showing that under certain conditions, the entanglement Hamiltonian can be interpreted as a thermal Hamiltonian with an effective temperature.

Contribution

It provides a rigorous condition for interpreting the entanglement Hamiltonian as a thermal Hamiltonian, clarifying the role of the coupling parameter as an inverse temperature.

Findings

Entanglement Hamiltonian is proportional to the energy Hamiltonian in strong coupling limit.

A condition is identified that guarantees the thermodynamic interpretation of entanglement Hamiltonian.

Illustrations include spin ladders and bilayer quantum Hall systems, showing close analogies to thermodynamics.

Abstract

We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement Hamiltonian is, in the limit of strong coupling between subsystems, proportional to the energy Hamiltonian of the subsystem. The proportionality factor is an appropriately defined coupling parameter, suggesting to interpret the latter as a inverse temperature. We identify a condition on the entanglement Hamiltonian which rigorously guarantees this interpretation to hold and removes any ambiguity in the definition of the entanglement Hamiltonian regarding contributions proportional to the unit operator. Illustrations of our findings are provided by spin ladders of arbitrary spin length, and by bilayer quantum Hall systems at total filling factor nu=2. Within mean-field description, the latter system realizes an entanglement spectrum of free fermions with just two levels of equal modulus where the analogies to canonical thermodynamics are particularly close.