A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases* *Supported by the National Natural Science Foundation of China under Grant No 11374331 and the key NSFC under Grant No 11534014. XWG has been partially supported by the Australian Research Council.

Abstract

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent ν = 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension.