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arXiv:0901.3555 · Physical Review A

Density-wave and antiferromagnetic states of fermionic atoms in optical lattices

Takuji Higashiyama, Kensuke Inaba, Sei-ichiro Suga

Published Feb 5, 2009• 3 citations
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Abstract

We study two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half filling an atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while an antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in the corresponding regions. By systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half filling. The results are discussed using the effective boson model derived for strong attractive interaction.

DOI
10.1103/physreva.79.023607

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We study two-band effects on ultracold fermionic atoms in optical lattices by means of dynamical mean-field theory. We find that at half filling an atomic-density-wave (ADW) state emerges owing to the two-band effects in the attractive interaction region, while an antiferromagnetic state appears in the repulsive interaction region. As the orbital splitting is increased, quantum phase transitions from the ADW state to the superfluid state and from the antiferromagnetic state to the metallic state occur in the corresponding regions. By systematically changing the orbital splitting and the interaction, we obtain the phase diagram at half filling. The results are discussed using the effective boson model derived for strong attractive interaction.
The superfluid-insulator transition of fermionic atoms in optical lattices is investigated by two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of multiband effects. The quasiparticle weight in the superfluid state decreases significantly as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.
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We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.
We study two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the magnetically ordered and superfluid states are not realized, but the metal-insulator transition occurs. This transition is characterized by the Mott and pairing transitions discussed in the conventional repulsive and attractive Hubbard models. In the doped system, commensurability emerges owing to the repulsive interactions and the metal-insulator transition occurs down to quarter-filling.
We investigate three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. Depending on the anisotropy of the repulsive interactions, either a color density-wave state or a color-selective staggered state appears at half filling. In the former state, pairs of atoms with two of the three colors and atoms with the third color occupy different sites alternately. In the latter state, atoms with two of the three colors occupy different sites alternately and atoms with the third color are itinerant throughout the system. When the interactions are isotropic, both states are degenerate. We discuss the results using an effective model.