Symmetry shapes thermodynamics of macroscopic quantum systems

Abstract

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We apply our technique to generic $N$ identical interacting $d$-level quantum systems. Using permutation invariance, we find that, for large $N$, entropy displays a universal large deviation behavior with a rate function $s(\mathbf{x})$ that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group ${\text{S}}_N$. In turn, the partition function is shown to satisfy a large deviation principle with a free energy $f(\mathbf{x})=e(\mathbf{x})-{\beta }^{-1}s(\mathbf{x})$, where $e(\mathbf{x})$ is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.

arXiv comment10 pages, 2 figures

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