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arXiv:2008.04588 · Physical Review A

Itinerant ferromagnetism in the repulsive Hubbard chain with spin-anisotropic odd-wave attraction

Manpreet Singh, Sebastiano Pilati, Giuliano Orso

Published Nov 3, 2020• 3 citations
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Abstract

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 nonlocal 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 occurs with the nucleation of a fully imbalanced band-insulating domain hosting the attractive component only. The size of this domain grows with the attraction strength, therefore increasing the (opposite) imbalance of the other domain, until the two spin components are fully separated. In the presence of a harmonic trap, the ferromagnetic state hosts a partially imbalanced domain in the center with an excess of the attractive component and filling lower than one. This central region is surrounded by fully imbalanced domains, located in the trap tails, hosting only fermions belonging to the other component.

DOI
10.1103/physreva.102.053301

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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 nonlocal attraction acts between fermions of one spin component only, mimicking the effect of ppp-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 occurs with the nucleation of a fully imbalanced band-insulating domain hosting the attractive component only. The size of this domain grows with the attraction strength, therefore increasing the (opposite) imbalance of the other domain, until the two spin components are fully separated. In the presence of a harmonic trap, the ferromagnetic state hosts a partially imbalanced domain in the center with an excess of the attractive component and filling lower than one. This central region is surrounded by fully imbalanced domains, located in the trap tails, hosting only fermions belonging to the other component.
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 UUU and spin imbalance ppp 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 UUU and ppp. 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 investigate the phase diagram of a two-component repulsive Fermi gas at T=0 by means of quantum Monte Carlo simulations. Both purely repulsive and resonant attractive model potentials are considered in order to analyze the limits of the universal regime where the details of interatomic forces can be neglected. The equation of state of both balanced and unbalanced systems is calculated as a function of the interaction strength and the critical density for the onset of ferromagnetism is determined. The energy of the strongly polarized gas is calculated and parametrized in terms of the physical properties of repulsive polarons, which are relevant for the stability of the fully ferromagnetic state. Finally, we analyze the phase diagram in the interaction-polarization plane under the assumption that only phases with homogeneous magnetization can be produced.
Using exact diagonalization techniques, the Hubbard model with hopping between nearest (t) and next-nearest neighbors ${(t}^{\ensuremath{'}})$ is studied in a two-dimensional cluster with $4\ifmmode\times\else\texttimes\fi{}4$ sites. Within a range of values of ${t}^{\ensuremath{'}}<0$ and low densities, states with different total spin are degenerate in the noninteracting system. At a finite value of the Coulomb repulsion U, states with high spin are energetically favored and the ground state can be fully polarized. The behavior of the density of states differs from that obtained within the Hartree-Fock approximation. The low energy region of the density of states (DOS) for the majority spins remains weakly modified by U. Our results bring further support to the idea that itinerant ferromagnetism occurs in strongly correlated systems with high noninteracting DOS at the bottom of the band.
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 carry out ab initio study of a ground state phase diagram of spin-1∕21∕21∕2 cold fermionic atoms within a twofold degenerate ppp band of an anisotropic optical lattice. Using the Gutzwiller variational approach, we show that a robust ferromagnetic phase exists for a vast range of band fillings and interacting strengths. The ground state crosses over from a spin density wave state to a spin-1 Neel state at half filling. An additional harmonic trap will induce spatial separation of various phases. We also discuss several relevant observable consequences and detection methods. An experimental test of the results reported here may shed some light on the long-standing issue of itinerant ferromagnetism.
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{U}_{c}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<UcU<{U}_{c}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{U}_{c}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.