Heat capacity for systems with excited-state quantum phase transitions

TL;DR

This paper investigates how excited-state quantum phase transitions cause anomalies in heat capacity calculations of finite quantum systems, revealing discrepancies between canonical and microcanonical approaches even at large sizes.

Contribution

It demonstrates the impact of excited-state quantum phase transitions on heat capacity calculations and highlights discrepancies between thermodynamic ensembles in such systems.

Findings

Microcanonical heat capacity exhibits a singularity at the transition

Canonical heat capacity shows a smooth but affected behavior

Discrepancies persist even in the infinite-size limit

Abstract

Heat capacities of model systems with finite numbers of effective degrees of freedom are evaluated using canonical and microcanonical thermodynamics. Discrepancies between both approaches, which are observed even in the infinite-size limit, are particularly large in systems that exhibit an excited-state quantum phase transition. The corresponding irregularity of the spectrum generates a singularity in the microcanonical heat capacity and affects smoothly the canonical heat capacity.