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Physical review. B./Physical review. B

Swap Mott transition in multicomponent fermion systems

Duc‐Anh Le, Thanh-Mai Thi Tran, Minh-Tien Tran

Published Mar 4, 2024• 1 citation
Publisher

Abstract

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 $SU(3)$ 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.

DOI
10.1103/physrevb.109.115105

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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.
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.
The mass-imbalanced Hubbard model represents a continuous evolution from the Hubbard to the Falicov-Kimball model. We employ dynamical mean field theory and study the paramagnetic metal-insulator transition, which has a very different nature for the two limiting models. Our results indicate that the metal-insulator transition rather resembles that of the Hubbard model as soon as a tiny hopping between the more localized fermions is switched on. At low temperatures we observe a first-order metal-insulator transition and a three peak structure. The width of the central peak is the same for the more and less mobile fermions when approaching the phase transition, which agrees with our expectation of a common Kondo temperature and phase transition for the two species.
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.
The effects of mass imbalance in a three-component Hubbard model are studied by the dynamical mean-field theory combined with exact diagonalization. The model describes a fermion-fermion mixture of two different particle species with a mass imbalance. One species is two-component fermion particles, and the other is single-component ones. The local interaction between particle species is considered isotropically. It is found that the mass imbalance can drive the mixture from insulator to metal. The insulator-metal transition is a species-selective-like transition of lighter mass particles and occurs only at commensurate particle densities and moderate local interactions. For weak and strong local interactions the mass imbalance does not change the ground state of the mixture.
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.
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.