Large deviations in mean-field quantum spin systems

TL;DR

This paper investigates large deviations in mean-field quantum spin systems using continuous $C^*$-bundles, providing a mathematical framework for understanding phase transitions and symmetry breaking in the macroscopic limit.

Contribution

It introduces a novel approach to analyze large deviations in mean-field quantum systems via continuous $C^*$-bundles generated by tensor powers of matrices.

Findings

Characterization of the limit of the logarithmic generating function.

Application of large deviations principle to high temperature regimes.

Framework for describing phase transitions in quantum spin systems.

Abstract

Continuous fields (or bundles) of $C^*$-algebras form an important ingredient for describing emergent phenomena, such as phase transitions and spontaneous symmetry breaking. In this work, we consider the continuous $C^*$-bundle generated by increasing symmetric tensor powers of the complex $\ell\times\ell$ matrices $M_\ell(\mathbb{C})$, which can be interpreted as abstract description of mean-field theories defining the macroscopic limit of infinite quantum systems. Within this framework we discuss the principle of large deviations for the local Gibbs state in the high temperature regime and characterize the limit of the ensuing logarithmic generating function.