We study the two-component repulsive Fermi gas with imbalanced populations in one dimension. Starting from the Bethe Ansatz solution we calculate analytically the phase diagram for the homogeneous system. We show that three phases appear: the balanced phase, the fully polarised phase and the partially polarised phase. By means of the local density approximation and the equation of state for the homogeneous system we calculate the density profile for the harmonically confined case. We show that a two-shell structure appears: at the center of the cloud we find the partially polarised phase and at the edges the fully polarised one. The radii of the inner and outer shells are calculated for different values of the polarisation and the coupling strength. We calculate the dependence of the magnetisation on the polarisation for different values of the coupling strength and we show that the susceptibility is always finite.
We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the one-dimensional homogeneous Gaudin-Yang model with Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchange-correlation interaction. By studyin…
We investigate the phase diagram of the one-dimensional repulsive Hubbard model with mass imbalance. Using DMRG, we show that this model has a "triplet" paired phase (dubbed $π\mathrm{SG}$) at generic fillings, consistent with previous theoretical analysis. We study the topological aspect of $π\mathrm{SG}$ phase, determining long-range string orders and the filling anomaly which refers to the relation among the single particle gap, inversion symmetry, and filling imbalance for open chains. We also find, using DMRG, that at $1/3$ filling, commensurate effects lead to two additional phases: a cr…
Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous g…
We numerically determine the very rich phase diagram of mass-imbalanced binary mixtures of hardcore bosons (or equivalently -- fermions, or hardcore-Bose/Fermi mixtures) loaded in one-dimensional optical lattices. Focusing on commensurate fillings away from half filling, we find a strong asymmetry between attractive and repulsive interactions. Attraction is found to always lead to pairing, associated with a spin gap, and to pair crystallization for very strong mass imbalance. In the repulsive case the two atomic components remain instead fully gapless over a large parameter range; only a very …
The ground-state properties of the Hubbard chain with on-site repulsion and anisotropic nearest-neighbor attraction are investigated by means of density matrix renormalization group calculations. The non-local attraction acts between fermions of one spin component only, mimicking the effect of p-wave Feshbach resonances in cold-atom systems. We analyze the onset of itinerant ferromagnetism, pinpointing the critical attraction strength where partially and fully ferromagnetic states occur. In the cold-atom setup, where the two (pseudo) spin populations are separately conserved, ferromagnetism oc…
The ground state phase diagram of the two-dimensional attractive Hubbard model with population imbalance is explored using a mean field ansatz. A linear programming algorithm is used to identify the blocked states, such that the population imbalance can be imposed exactly. This allows to explore regions of the number-projected phase diagram that can not be obtained with the conventional Bogoliubov-de Gennes ansatz. The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase of pairs with non-zero momentum is found to be the ground state over a wide range of parameters, while phase separation occurs only …
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 paper we perform unrestricted Hartree-Fock calculations for the 2D case and find that above a critical interaction strength $U_c$ the system turns ferromagnetic at the edge of the trap, in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For $U<U_c$ we find a canted antifer…
We investigate ferromagnetic ordering in an itinerant ultracold atomic Fermi gas with repulsive interactions and population imbalance. In a spatially uniform system, we show that at zero temperature the transition to the itinerant magnetic phase transforms from first to second order with increasing population imbalance. Drawing on these results, we elucidate the phases present in a trapped geometry, finding three characteristic types of behavior with changing population imbalance. Finally, we outline the potential experimental implications of the findings.
We propose a Real-Space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin 1/2 trapped in an optical lattice with a harmonic confinement. Using the Real-Space Gutzwiller variational approach, we find that in system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring and antiferromagnetic order is stable in the regions where the particle density is close to one, which is consistent with the recent results obtained by the Real-Space Dynamical Mean-field Theory ap…
We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in the strongly and weakly interacting limits can be accurately described using wave function factorized in hyperspherical coordinates. Inspired by this result we propose an interpolation ansatz for the wave function for arbitrary repulsive zero-range interactions. By comparison to numerical calculations, …
We investigate effects of pseudo-spin population imbalance on Mott phases in 1D 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 pseudo-spin 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 …
We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. Using dynamical mean-field theory, we study the transition from a fluid to a Mott insulator driven by the repulsive interactions. For almost every value of the parameters we find that the light species with smaller bare mass is more affected by correlations than the heavy one, so that their effective masses become closer than their bare masses before a Mott transition occurs. The strength of the critical repulsion decreases monotonically as the mass imbalance grows so that the minimum is realized w…
We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attr…
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose-Fermi and Fermi-Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron …
A repulsive Hubbard model with both spin-asymmetric hopping (${t_\uparrow\neq t_\downarrow}$) and a staggered potential (of strength $Δ$) is studied in one dimension. The model is a compound of the mass-imbalanced (${t_\uparrow\neq t_\downarrow}$, ${Δ=0}$) and ionic (${t_\uparrow = t_\downarrow}$, ${Δ>0}$) Hubbard models, and may be realized by cold atoms in engineered optical lattices. We use mostly mean-field theory to determine the phases and phase transitions in the ground state for a half-filled band (one particle per site). We find that a period-two modulation of the particle (or charge)…
We explore the phases exhibited by an interacting quantum spin Hall edge state in the presence of finite chemical potential (applied gate voltage) and spin imbalance (applied magnetic field). We find that the helical nature of the edge state gives rise to orders that are expected to be absent in non-chiral one-dimensional electronic systems. For repulsive interactions, the ordered state has an oscillatory spin texture whose ordering wavevector is controlled by the chemical potential. We analyze the manner in which a magnetic impurity provides signatures of such oscillations. We find that finit…
We describe the dynamics of two component non-interacting ultracold Fermions which are initially in thermal equilibrium and undergo a rapid quench to either the repulsive or attractive side of a Feshbach resonance. The short time dynamics is dominated by the exponentially growing collective modes. We study the Stoner instability and formation of ferromagnetic textures on the repulsive side, and the pairing instability towards BCS or FFLO-like states (determined by the population imbalance) on the attractive side. In each case, we evaluate the growth rate of unstable modes and predict the typic…
We investigate the phase separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of density-matrix renormalization method. The phase separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between intercomponent fermions. We find the existence of a critical repulsive interaction strength above which the phase separation evolves. By increasing the trap imbalance, the composite phase of Mott-insulating core is changed in…
We study a two species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive interaction. Such a model can be realized in a cold atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable inter-species interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities fo…
We theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local density approximation. We demonstrate that, while the local density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase tra…
