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Communications in Physics

Metal-insulator Transitions in Three-component Falicov-Kimball Model within Coherent Potential Approximation

Thi Huong Nguyen, Tuan Hoang Anh, Duc Anh Le

Published Nov 3, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.15625/0868-3166/17244

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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.
Metal-insulator transitions in a three-component Falicov-Kimball model are investigated within the Kotliar-Ruckenstein slave boson mean-field approach. The model describes a mixture of two interacting fermion atom species loaded into an optical lattice at ultralow temperature. One species is two-component atoms, which can hop in the optical lattice, and the other is single-component atoms, which are localized. Different correlation-driven metal-insulator transitions are observed depending on the atom filling conditions and local interactions. These metal-insulator transitions are classified by the band renormalization factors and the double occupancies of the atom species. The filling conditions and the critical value of the local interactions for these metal-insulator transitions are also analytically established. The obtained results not only are in good agreement with the dynamical mean-field theory for the three-component Falicov-Kimball model but also clarify the nature and properties of the metal-insulator transitions in a simple physics picture.
Metal-insulator transitions in an asymmetric three-component Falicov-Kimball model are investigated within the two-site dynamical mean field theory. The model is obtained from the symmetry breaking of the SU(3)SU(3)SU(3) Hubbard model by imbalanced masses and nonequal local interactions of particle components. The Mott transitions are classified by the change in the number of distinct kinds of doublons across the transition. We observe a different Mott transition between partially localized states in which the particle components (flavors), which form the doublons, are swapped with each other but the number of distinct kinds of doublons is unchanged across the transition. The swap Mott transition occurs as a result of the competition between the Brinkman-Rice and the Falicov-Kimball localizations and the mass imbalance of the mobile particles.
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.
The ground-state phase diagrams of the Falicov-Kimball model with local disorder are derived within the dynamical mean-field theory and using the geometrically averaged (``typical'') local density of states. Correlated metal, Mott insulator, and Anderson insulator phases are identified. The metal-insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against the occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.