Wilson ratio of Fermi gases in one dimension
Dr Xiwen Guan
In this talk, I will discuss the Wilson ratio of a one-dimensional (1D) Fermi gas (the Yang-Gaudin model) with spin imbalance. For attractive interaction, we find that the Wilson ratio, involving the spin susceptibility and specific heat, exhibits anomalous divergence near the two critical points due to a sudden change of the density of state. For an intermedium magnetic field, the ratio indicates a universal nature of a two-component Tomonaga-Luttinger liquid (TLL) of the Fulde-Ferrel-Larkin-Ovchinnikov-like pairing phase. Despite a breakdown of the quasiparticle nature in 1D, two important signatures of the Fermi liquid (FL) are retained, namely the specific heat is linearly proportional to the temperature, whereas the susceptibility is independent of temperature. These quantities are solely determined by two stiffnesses of pairs and excess fermions in the TLL phase. We see that an analog for the zero temperature susceptibility of the gapless phase is two parallel resistors in a circuit. For the repulsive regime, the Wilson ratio simply gives a fixed point of the TLL in the scenario of spin-charge separation. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions. We also discuss the pairing nature in spin-3/2 Fermi gases of cold atoms.