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International Conference on Strongly Correlated Electron Systems (SCES)

Ferromagnetism in Multi-Orbital Fermi Gas Loaded on a One-Dimensional Optical Lattice

Keita Kobayashi, Masahiko Okumura, Yukihiro Ota, Susumu Yamada, Masahiko Machida

Published Jun 16, 2014• 0 citations
Publisher

Abstract

We study a multi-orbital Fermi gas loaded on a one-dimensional optical lattice with harmonic trap potential. We show that this multi-orbital gas contains various quantum phases, i.e., (i) the ferromagnetic phase in large on–site interaction and (ii) the Haldane phase at half filling. Furthermore, our density-matrix renormalization-group simulations lead to systematic studies about the ground state, varying on–site interaction, spin imbalance, and total particle number, under spatial inhomogeneity originating from the trap potential. This trap potential produces a rich phase structure. In a metallic region, the phase-separated ferromagnetism appears, whereas in a central Mott core the Haldane phase is found. One of the remarkable features is that the ferromagnetic metal phase behaves as the edge state of the Haldane phase when these two phases coexist.

DOI
10.7566/jpscp.3.016006

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We study a multi-orbital Fermi gas loaded on a one-dimensional optical lattice with harmonic trap potential. We show that this multi-orbital gas contains various quantum phases, i.e., (i) the ferromagnetic phase in large on–site interaction and (ii) the Haldane phase at half filling. Furthermore, our density-matrix renormalization-group simulations lead to systematic studies about the ground state, varying on–site interaction, spin imbalance, and total particle number, under spatial inhomogeneity originating from the trap potential. This trap potential produces a rich phase structure. In a metallic region, the phase-separated ferromagnetism appears, whereas in a central Mott core the Haldane phase is found. One of the remarkable features is that the ferromagnetic metal phase behaves as the edge state of the Haldane phase when these two phases coexist.
We propose a method to create a nontrivial Haldane phase in an atomic two-component Fermi gas loaded on a one-dimensional optical lattice with trap potential. The Haldane phase is naturally formed on a p-band Mott core in a wide range of the strong on-site repulsive interaction. The present proposal is composed of two steps, one of which is theoretical derivation of an effective 1D S=1 interacting-chain model from the original tight-binding Hamiltonian handling the two p orbitals, and the other of which is a numerical demonstration employing the density-matrix renormalization group for the formation of the Haldane phase on a p-band Mott core and its associated features in the original tight-binding model with the harmonic trap potential.
We examine quantum phases emerging from the double degeneracy of ppp-orbital bands in attractive atomic Fermi gases loaded on a one-dimensional (1D) optical lattice. Our numerical simulations via the density-matrix renormalization group predict the emergence of a state with a charge excitation gap, namely the Haldane insulator phase. A mapping onto an effective spin-1 model reveals its physical origin. Moreover, we show that population imbalance leads to richer diversity of the quantum phases, including a phase-separated polarized state. Finally, we study the effects of the harmonic trap potential in this 1D chain.
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 separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of the 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 the Mott-insulating core is changed into one of the ferromagnetic insulating core, which is incompressible and originates from the Pauli exclusion principle.
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.
We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.