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Journal of Physics Conference Series

Perturbative approach to three-component fermionic atoms in optical lattices

Sei-ichiro Suga, Kensuke Inaba

Published Dec 14, 2012• 1 citation
Publisher

Abstract

We develop a perturbative approach combined with the dynamical mean-field theory for investigating the Mott transition in repulsively interacting three-component fermionic atoms in optical lattices. We show that this method captures the essentials of the correlation effects and describes well the crossover between the Fermi liquid and the paired Mott insulator.

DOI
10.1088/1742-6596/391/1/012166

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We develop a perturbative approach combined with the dynamical mean-field theory for investigating the Mott transition in repulsively interacting three-component fermionic atoms in optical lattices. We show that this method captures the essentials of the correlation effects and describes well the crossover between the Fermi liquid and the paired Mott insulator.
We investigate the Mott transitions of three-component (colors) repulsive fermionic atoms in optical lattices using the dynamical mean-field theory. We find that for SU(3) symmetry-breaking interactions, the Mott transition occurs at incommensurate half filling. As a result, a characteristic Mott insulating state appears, where paired atoms with two different colors and atoms with the third color are localized, and either of these states is randomly distributed in each site. We also find another Mott state, where atoms with two different colors are randomly localized at different sites, and atoms with the third color remain itinerant. We demonstrate that double occupancy measurements show characteristics of these exotic Mott phases.
We investigate finite-temperature properties of three-component (color) repulsive fermionic atoms in optical lattices at half filling using a self-energy functional approach. For a certain anisotropy of the interactions, we find a color density-wave (DW) state at low temperatures. In the weakly interacting region, the second-order phase transition from the color DW state to the Fermi-liquid state occurs with increasing temperature. In the strongly interacting region, by contrast, the first-order transition from the color DW state to a color selective Mott transition (CSMT) state or a Mott insulating state occurs. As the interaction increases above the critical temperatures, we observe a crossover from the CSMT state to the Mott insulating state.
We investigate the effects of a repulsive three-body interaction on the Mott transition of the repulsively interacting three-component fermionic atoms in optical lattices by means of the self-energy functional approach. We find that the three-body repulsion hardly affects the qualitative features of the Mott transition, because the three-body repulsion does not compete with the two-body repulsions. When the three-body repulsion is extremely strong, the triple occupancy vanishes in the Fermi liquid state. This situation is equivalent to that caused by strong three-body losses. Our results imply that three-body losses have little influence on the Mott transitions in the repulsively interacting three-component fermionic atoms in optical lattices.
We apply the coherent potential approximation to study the three-component Falicov - Kimball model, in which single-component and two-component fermionic particles are mixed in an optical lattice. In the model, the heavy single-component fermionic particles are localized while the light two-component fermionic particles can hop in the lattice. At half-filling, two transitions from an insulator via a metallic state to a Mott insulator are found with increasing the particle correlations. By contrast, at third-filling, only one transition from the metallic state to the Mott insulating phase is observed for strong repulsive interactions. Our results are consistent with those obtained by the dynamical mean field theory as well as by the slave boson mean field approach.
Metal-insulator transitions are studied within a three-component Falicov-Kimball model, which mimics a mixture of one-component and two-component fermionic particles with local repulsive interactions in optical lattices. Within the model, the two-component fermionic particles are able to hop in the lattice, while the one-component fermionic particles are localized. The model is studied by using the dynamical mean-field theory with exact diagonalization. Its homogeneous solutions establish Mott transitions for both commensurate and incommensurate fillings between one-third and two-thirds. At commensurate one-third and two-thirds fillings, the Mott transition occurs for any density of hopping particles, while at incommensurate fillings, the Mott transition can occur only for density one-half of hopping particles. At half-filling, depending on the repulsive interactions, the reentrant effect of the Mott insulator is observed. As increasing local interaction of hopping particles, the first insulator-metal transition is continuous, whereas the second metal-insulator transition is discontinuous. The second metal-insulator transition crosses a finite region where both metallic and insulating phase coexist. At third-filling, the Mott transition is established only for strong repulsive interactions. A phase separation occurs together with the phase transition.
We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean-field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.