Thermal Area Law for Lattice Bosons

TL;DR

This paper establishes a thermal area law for lattice bosons, including the Bose-Hubbard model, by introducing a quasi-free reference state and overcoming challenges posed by unbounded interactions.

Contribution

It provides the first rigorous derivation of a thermal area law for unbounded lattice bosonic systems, extending previous results from spin systems.

Findings

Proves a thermal area law for a class of bosonic Hamiltonians.

Uses a double Peierls-Bogoliubov estimate to handle unbounded interactions.

Includes the paradigmatic Bose-Hubbard model in the analysis.

Abstract

A physical system is said to satisfy a thermal area law if the mutual information between two adjacent regions in the Gibbs state is controlled by the area of their boundary. Thermal area laws have been derived for systems with bounded local interactions such as quantum spin systems. However, for lattice bosons these arguments break down because the interactions are unbounded. We rigorously derive a thermal area law for a class of bosonic Hamiltonians in any dimension which includes the paradigmatic Bose-Hubbard model. The main idea to go beyond bounded interactions is to introduce a quasi-free reference state with artificially decreased chemical potential by means of a double Peierls-Bogoliubov estimate.