Divergence of the Gr\"uneisen ratio at symmetry-enhanced first-order quantum phase transitions

TL;DR

This paper demonstrates that the Gr"uneisen ratio diverges at symmetry-enhanced first-order quantum phase transitions with mean-field exponents, expanding its applicability beyond continuous transitions.

Contribution

It reveals that the Gr"uneisen ratio diverges at certain first-order quantum phase transitions due to symmetry enhancement, supported by explicit pseudo-spin model analyses.

Findings

Gr"uneisen ratio diverges at symmetry-enhanced first-order transitions

Divergence follows mean-field exponents due to mode gap vanishing

Implications for quantum criticality studies and experimental detection

Abstract

Studies of the Gr\"uneisen ratio, i.e., the ratio between thermal expansion and specific heat, have become a powerful tool in the context of quantum criticality, since it was shown theoretically that the Gr\"uneisen ratio displays characteristic power-law divergencies upon approaching the transition point of a continuous quantum phase transition. Here we show that the Gr\"uneisen ratio also diverges at a symmetry-enhanced first-order quantum phase transition, albeit with mean-field exponents, as the enhanced symmetry implies the vanishing of a mode gap which is finite away from the transition. We provide explicit results for simple pseudo-spin models, both with and without Goldstone modes in the stable phases, and discuss implications.