Free energy density for mean field perturbation of states of a one-dimensional spin chain

TL;DR

This paper extends the variational expression of free energy density for one-dimensional spin chains from product states to Gibbs states with translation-invariant interactions, clarifying relations in quantum Markov states.

Contribution

It generalizes previous results to Gibbs states and explores the connection between different free energy densities in quantum Markov states.

Findings

Extended variational formula to Gibbs states with finite-range interactions

Clarified relation between free energy densities in quantum Markov states

Provided theoretical framework for large deviations in spin chain states

Abstract

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).