A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive $SU(w)$ Fermi Gases
Yi-Cong Yu, Xi-Wen Guan**
1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 2University of Chinese Academy of Sciences, Beijing 100049 3Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071 4Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
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 $\nu=1/2$. 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.
2017, Vol. 34 
