Universal low-energy physics in 1D strongly repulsive multi-component Fermi gases

It has been shown (Yang and You 2011 Chin. Phys. Lett. 28 020503) that at zero temperature the ground state of the one-dimensional (1D) w-component Fermi gas coincides with that of the spinless Bose gas in the limit w → ∞. This behavior was experimentally evidenced through quasi-1D tightly trapping ultracold ¹⁷³Yb atoms in a recent paper (Pagano et al 2014 Nat. Phys. 10 198). However, understanding of low-temperature behavior of Fermi gases with a repulsive interaction requires spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(w) Heisenberg spin chain. Here we analytically derive universal thermodynamics of 1D strongly repulsive fermionic gases with SU(w) symmetry via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the systems at low temperature in a weak magnetic field are obtained through the Wiener-Hopf method. In particular, the free energy essentially manifests the spin-charge separated conformal field theories for high-symmetry systems with arbitrary repulsive interaction strength. We also find that the sound velocity of the Fermi gases in the large w limit coincides with that for the spinless Bose gas, whereas the spin velocity vanishes quickly as w becomes large. This indicates strong suppression of the Fermi exclusion statistics by the commutativity feature among the w-component fermions with different spin states in the Tomonaga-Luttinger liquid phase. Moreover, the equations of state and critical behavior of physical quantities at finite temperature are analytically derived in terms of the polylogarithm functions in the quantum critical region.