We investigate effects of pseudospin population imbalance on Mott phases in one-dimensional trapped two-component atomic Fermi gases loaded on optical lattices based on the repulsive Hubbard model in harmonic traps. By using the density-matrix renormalization-group method, we numerically calculate density profiles of each component and clarify the pseudospin magnetism. Consequently, we find that all the features from weakly imbalance to fully polarized cases are well described by
S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.
We investigate effects of optical lattice potential in one- and two-dimensional two-component trapped Fermi gases with population imbalances. Using the exact diagonalization and the density matrix renormalization group methods complementarily, we calculate the atom-density profile from the ground state many-body wave function as a function of attractive interaction strength for various population imbalances. The numerical results reveal that although a phase separation between the superfluid core and the shell cloud of excess atoms occurs as observed in experiments without the optical lattice, the population imbalance generally remains in the core region in contrast to the nonlattice cases. The essence of the numerical results in a strong attractive regime can be explained by an effective model composed of Cooper pairs and excess major fermions.
We analyze the repulsive fermionic Hubbard model on square and cubic lattices with spin imbalance and in the presence of a parabolic confinement. We analyze the magnetic structure as a function of the repulsive interaction strength and polarization. In the first part of the article, we perform unrestricted Hartree-Fock calculations for the two-dimensional (2D) case and find that above a critical interaction strength
Uc the system turns ferromagnetic at the edge of the trap, which is in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For
U<Uc, we find a canted antiferromagnetic structure in the Mott region in the center and a partially polarized compressible edge. The antiferromagnetic order in the Mott plateau is perpendicular to the direction of the imbalance. In this regime, the same qualitative behavior is expected for 2D and three-dimensional (3D) systems. In the second part of the article, we give a general discussion of magnetic structures above
Uc. We argue that spin conservation leads to nontrivial textures, both in the ferromagnetic polarization at the edge and for the N\'eel order in the Mott plateau. We discuss differences in magnetic structures for 2D and 3D cases.
We consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction
U and spin imbalance
p in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough
U and
p. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.
We use a combination of numerical density matrix renormalization group calculations and several analytical approaches to comprehensively study a simplified model for a spatially anisotropic spin-
21 triangular lattice Heisenberg antiferromagnet: the three-leg triangular spin tube (TST). The model is described by three Heisenberg chains, with exchange constant
J, coupled antiferromagnetically with exchange constant ${J}^{\ensuremath{'}}$ along the diagonals of the ladder system, with periodic boundary conditions in the shorter direction. Here, we determine the full phase diagram of this model as a function of both spatial anisotropy (between the isotropic and decoupled chain limits) and magnetic field. We find a rich phase diagram, which is remarkably dominated by quantum states: the phase corresponding to the classical ground state appears only in an exceedingly small region. Among the dominant phases generated by quantum effects are commensurate and incommensurate coplanar quasiordered states, which appear in the vicinity of the isotropic region for most fields, and in the high-field region for most anisotropies. The coplanar states, while not classical ground states, can at least be understood semiclassically. Even more strikingly, the largest region of phase space is occupied by a spin density wave phase, which has incommensurate collinear correlations along the field. This phase has no semiclassical analog, and may be ascribed to enhanced one-dimensional fluctuations due to frustration. Cutting across the phase diagram is a magnetization plateau, with a gap to all excitations and ``up-up-down'' spin order, with a quantized magnetization equal to
31 of the saturation value. In the TST, this plateau extends almost but not quite to the decoupled chains limit. Most of the above features are expected to carry over to the two-dimensional system, which we also discuss. At low field, a dimerized phase appears, which is particular to the one-dimensional nature of the TST, and which can be understood from quantum Berry phase arguments.
We investigate the magnetic shell structure of repulsively interacting two-component Fermi gases trapped in a two-dimensional harmonic potential and loaded on the optical Lieb lattices. We employ the real-space dynamical mean-field theory (R-DMFT) to explicitly consider the trap potential in a self-consistent way. Computing the profiles of particle density and local magnetization across the lattice sites in the trap, we find that the incompressible core with ferrimagnetic ordering appears with the density plateau at the trap center, which is surrounded by the shell of the normal metallic phase. We examine the incompressibility of the core by adding more particles and creating the higher spin-population imbalance. While the core area expands from the outer shell with added particles and increased polarization, the excess particles are prohibited from going inside the core, and thus the density plateau is unchanged at the half-filling with the same magnetic ordering. In addition, we find that the feature of the phase separation differs with the sublattices, where the interstitial sites causing the flat band dispersion shows the signature of the abrupt transition in the density and magnetization at the boundary between the core and surrounding shells.