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arXiv:1008.3055 · Physical Review A

Phase-separated ferromagnetism in a spin-imbalanced system of Fermi atoms loaded in an optical ladder: A density-matrix renormalization-group study

Masahiko Okumura, S. Yamada, Masahiko Machida, Hideo Aoki

Published Mar 9, 2011• 16 citations
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Abstract

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.

DOI
10.1103/physreva.83.031606

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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 calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local-density approximation (LDA) and density-matrix renormalization-group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, the LDA predicts that the gas phase separates into shells with a partially polarized core and fully paired wings, the latter occurring below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. We show that, unlike in the continuum case, the critical polarization is a nonmonotonic function of the interaction strength and vanishes in the limit of large interactions.
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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=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.
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.
In order to study an interplay of disorder, correlation, and spin imbalance on antiferromagnetism, we systematically explore the ground state of one-dimensional spin-imbalanced Anderson-Hubbard model by using the density-matrix renormalization-group method. We find that disorders localize the antiferromagnetic spin-density wave induced by imbalanced fermions and the increase in the disorder magnitude shrinks the areas of the localized antiferromagnetized regions. Moreover, the antiferromagnetism finally disappears above a large disorder. The localization behaviors are observable in atomic Fermi gases loaded on optical lattices as broadening of the momentum distribution of the spin density by using the Stern-Gerlach type of time-of-flight imaging.