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.
We investigate the metal-insulator transition of the one-dimensional
SU(N) Hubbard model for repulsive interaction. Using the bosonization approach a Mott transition in the charge sector at half filling ${(k}_{F}=\ensuremath{\pi}{/Na}_{0})$ is conjectured for
N>2. Expressions for the charge and spin velocities as well as for the Luttinger-liquid parameters and some correlation functions are given. The theoretical predictions are compared with numerical results obtained with an improved zero-temperature quantum Monte Carlo approach. The method used is a generalized Green's function Monte Carlo scheme in which the stochastic time evolution is partially integrated out. Very accurate results for the gaps, velocities, and Luttinger-liquid parameters as a function of the Coulomb interaction
U are given for the cases
N=3 and
N=4. Our results strongly support the existence of a Mott-Hubbard transition at a nonzero value of the Coulomb interaction. We find ${U}_{c}\ensuremath{\sim}2.2$ for
N=3 and ${U}_{c}\ensuremath{\sim}2.8$ for
N=4.In this article we study a generalized
t−J model in which we dope spin-one doublons into a spin
1/2 Mott insulator. We generalize this model to
SU(N) case and obtain the ground state based on a three-fermion parton mean field calculation. Surprisingly, for almost every doping we find a fractional Fermi liquid (FL*) phase , which is a symmetric pseudogap metal in the sense that the total Fermi volume is equal to
x, instead of
1+x as required by Luttinger constraint of a Fermi liquid. We then verify our theory in one dimension through DMRG simulation of the
t−J model. Indeed we find that the doped doublon forms a small Fermi on top of the spinon Fermi surface (
SU(2)1 CFT) inherited from the Mott insulator. This phase is clearly a one dimension analog of the FL* phase and we dub it as fractional Luttinger liquid (LL*). We also discover a continuous quantum phase transition from this LL* phase with small Fermi to conventional Luttinger liquid phase with large Fermi by tuning interaction strength in a two-orbital Hubbard model at fixed density. Lastly we discuss the experimental realizations of this generalized
t−J model and comment on possible connection to the recently discovered nickelate superconductor Nd
1−xSr
xNiO
2.