Gr\"uneisen parameters for Lieb-Liniger and Yang-Gaudin models

TL;DR

This paper analytically investigates the Gr"uneisen parameters in 1D Lieb-Liniger and Yang-Gaudin models, revealing their universal scaling near quantum critical points and their role in identifying quantum phases and transitions.

Contribution

It provides the first analytical study of expansionary, magnetic, and interacting Gr"uneisen parameters in these models, linking them to quantum criticality and phase transitions.

Findings

Universal scaling behavior of GPs near quantum critical points

Divergence of GPs identifies non-Fermi liquid behavior

Magnetic and interacting GPs capture pairing and depairing in Fermi gases

Abstract

Using the Bethe ansatz solution, we analytically study expansionary, magnetic and interacting Gr\"uneisen parameters (GPs) for one-dimensional (1D) Lieb-Liniger and Yang-Gaudin models. These different GPs elegantly quantify the dependences of characteristic energy scales of these quantum gases on the volume, the magnetic field and the interaction strength, revealing the caloric effects resulted from the variations of these potentials. The obtained GPs further confirm an identity which is incurred by the symmetry of the thermal potential. We also present universal scaling behavior of these GPs in the vicinities of the quantum critical points driven by different potentials. The divergence of the GPs not only provides an experimental identification of non-Fermi liquid nature at quantum criticality but also elegantly determine low temperature phases of the quantum gases. Moreover, the pairing and depairing features in the 1D attractive Fermi gases can be captured by the magnetic and interacting GPs, facilitating experimental observation of quantum phase transitions. Our results open to further study the interaction- and magnetic-field-driven quantum refrigeration and quantum heat engine in quantum gases of ultracold atoms.