Grüneisen parameters for the Lieb-Liniger and Yang-Gaudin models

Using the Bethe ansatz solution, we analytically study expansionary, magnetic, and interacting Grüneisen parameters (GPs) for one-dimensional (1D) Lieb-Liniger and Yang-Gaudin models. These different GPs elegantly quantify the dependence of characteristic energy scales of these quantum gases on the volume, the magnetic field, and the interaction strength, revealing the caloric effects resulting 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 the 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 determines 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 the way to further study the interaction- and magnetic-field-driven quantum refrigeration and quantum heat engine in quantum gases of ultracold atoms.