Universal low energy physics in one-dimensional multicompnent Fermi gases with a strongly repulsive $\delta$-function interaction

Abstract

It was shown [Chin. Phys. Lett. 28, 020503 (2011)] 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 $\omega \to \infty$. This behaviour was experimentally evidenced through a quasi-1D tightly trapping ultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198 (2014)]. However, understanding of low temperature behaviour of the Fermi gases with a repulsive interaction acquires 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 temperatures 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 the 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 a 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 behaviour of physical quantities at finite temperatures are analytically derived in terms of the polylogarithm functions in the quantum critical region.

arXiv comment26 pages 3 figures, solid calculation of low energy physical properties of SU(w) Fermi gases

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• Evidence for Bosonization in a three-dimensional gas of SU($N$) fermions
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
• Spectroscopy and spin dynamics for strongly interacting few spinor bosons in one-dimensional traps
• A unified approach to the thermodynamics and quantum scaling functions of one-dimensional strongly attractive $SU(w)$ Fermi Gases
• Impurity immersed in a two-component few-fermion mixture in a one-dimensional harmonic trap