Wilson Ratios and Quantum Liquids
The Wilson ratio, defined as the ratio of magnetic susceptibility over heat capacity divided by temperature, could be used to characterize low temperature phases of a wide variety of materials. It was successfully applied to the study resistivity minimum observed in metal when doped with magnetic impurity. Replacing susceptibility by compressibility, we also introduced another Wilson ratio to account for particle number fluctuation. Using experimentally realized multi-species cold atomic gases as examples, we show that the Wilson ratios uniquely identify phases of quantum liquids, while providing universal scaling relations at the boundaries between phases. Since these WRs are composed of direct measurable thermodynamic quantities, our findings provide an easy way to map out quantum phases experimentally.