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arXiv:1812.08677 · Physical Review A

One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction

Denis V. Kurlov, Sergey I. Matveenko, Vladimir Gritsev, Georgy V. Shlyapnikov

Published Apr 29, 2019• 3 citations
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Abstract

We consider a one-dimensional two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2)-symmetry-breaking near-resonant odd- wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

DOI
10.1103/physreva.99.043631

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We consider a one-dimensional two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2)-symmetry-breaking near-resonant odd- wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.
We study a one-dimensional (1D) two-component atomic Fermi gas with an infinite intercomponent contact repulsion. It is found that adding an attractive nearly resonant odd-wave interaction breaking the rotational symmetry one can make the ground state ferromagnetic. A promising system for the observation of this itinerant ferromagnetic state is a 1D gas of 40K^{40}\mathrm{K}40K atoms, where three dimensional sss-wave and ppp-wave Feshbach resonances are very close to each other and the 1D confinement significantly reduces the inelastic decay.
We consider a gas of fermions with parabolic dispersion and N spin components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. The ground-state Bethe ansatz integral equations are solved numerically for both repulsive and attractive interactions to obtain the energy, the chemical potential, and the magnetic susceptibility as a function of the band filling and the interaction strength. For the repulsive interaction the Fermi gas has the properties of a Luttinger liquid. In the attractive case, on the other hand, the fermions in the ground-state form bound states of up to N fermions of different spin components. The spectrum of elemental charge and spin excitations is derived for the repulsive and attractive situations. The spectrum is discussed in the limits of vanishing interaction strength and very strong coupling. For the repulsive interaction the low-lying charge excitations can be characterized by the Fermi momentum and the Fermi velocity. The range of the spin-wave excitations is correlated with the Fermi momentum of the charges. The spin wave velocity is inversely proportional to the magnetic susceptibility. The spin-wave excitations become soft in the infinite-repulsive-coupling limit. In the attractive case in zero field all excitation branches except that of bound states of N fermions have an energy gap. It requires a finite energy to break these bound states and hence there is no response to a field smaller than a critical field. The low-T specific heat is proportional to the temperature.
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The two- and three-body correlation functions of the ground state of an optically trapped ultracold spin-12\frac{1}{2}21​ Fermi gas (SFG) in a tight waveguide [one-dimensional (1D) regime] are calculated in the plane of even- and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D ppp-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D sss-wave scattering. The calculations are based on the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg'' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas, a spin-aligned 1D Fermi gas with infinitely attractive ppp-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.
We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k F → 4k F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.