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arXiv:cond-mat/0402170 · Physical Review Letters

Effect of Particle-Hole Asymmetry on the Mott-Hubbard Metal-Insulator Transition

D. O. Demchenko, A. V. Joura, James K. Freericks

Published May 28, 2004• 15 citations
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Abstract

The Mott-Hubbard metal-insulator transition is one of the most important problems in correlated-electron systems. In the past decade, much progress has been made in examining a particle-hole symmetric form of the transition in the Hubbard model with dynamical mean field theory, where it was found that the electronic self-energy develops a pole at the transition. We examine the particle-hole asymmetric metal-insulator transition in the Falicov-Kimball model and find that a number of features change when the noninteracting density of states has a finite bandwidth.

DOI
10.1103/physrevlett.92.216401

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The Mott-Hubbard metal-insulator transition is one of the most important problems in correlated-electron systems. In the past decade, much progress has been made in examining a particle-hole symmetric form of the transition in the Hubbard model with dynamical mean field theory, where it was found that the electronic self-energy develops a pole at the transition. We examine the particle-hole asymmetric metal-insulator transition in the Falicov-Kimball model and find that a number of features change when the noninteracting density of states has a finite bandwidth.
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 statistical dynamical mean field theory is used to study the metal-insulator transition in the two-dimensional Falicov-Kimball model with local disorder. Within the theory, the local density of states and its distributions are calculated. As a measure of the metal-insulator transition driven by correlation and disorder, the most probable value of the local density of states is determined. The most probable value of the local density of states is found to exhibit a discontinuity when the system crosses from extended states to localization. A phase diagram is also presented.
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.
Starting from the standard Hubbard model, this paper obtained an asymmetric Hamiltonian for the half-filled strongly correlated system by ignoring the jumping of electrons with spin-σ between lattice sites when the motion of electrons with spin σ is considered. The mean field approximation is applied to get the quasi-particle spectrum of the Hamiltonian. The results at zero-temperature and finite temperature are analyzed,the possibility and critical temperature of Mott metal-insulator transition is also investigated.
The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.
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.