Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach

TL;DR

This paper uses a grand canonical approach to identify thermodynamic signatures of quantum phase transitions, revealing divergence patterns and observable indicators that can detect critical points without reaching zero temperature.

Contribution

It introduces a grand canonical formalism to analyze quantum phase transitions and derives analytical expressions for thermodynamic observables indicating criticality.

Findings

Grand partition function diverges with a power law near the critical point

Power-law exponent uniquely identifies the quantum critical point

Thermodynamic observables can signal the transition without zero temperature

Abstract

The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.