Quantum criticality of a one-dimensional attractive Fermi gas

We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gases for all parameter regimes in current experiments. From the equation of state, we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate the physical origin of quantum criticality. It turns out that the critical properties of the system are described by those of free fermions and those of mixtures of fermions with masses m and 2m. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gases at finite temperatures and can be used to determine the T=0 phase boundaries without any arbitrariness.