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arXiv:1611.10079 · The European Physical Journal B

Mott-Hubbard transition in the mass-imbalanced Hubbard model

Marie-Therese Philipp, Markus Wallerberger, Patrik Gunacker, Karsten Held

Published Jun 1, 2017• 10 citations
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Abstract

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.

DOI
10.1140/epjb/e2017-80115-7

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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.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
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 Hubbard model (HM) and the Falicov-Kimball model (FKM), which are two standard models of strongly correlated electrons, provide an interesting benchmark for the physics of locally correlated systems. We study the intermediate model, mass-imbalanced Hubbard model at half-filling on a 2D square lattice which connects continuously the HM to the FKM.We employ dynamical mean field theory (DMFT) and dynamical cluster approximation (DCA) using continuous-time auxiliary field method (CT-AUX) as self-consistent impurity solver to study the single particle spectral function and self-energy allowing us to map-out the phase diagram of the system. Solutions to the mass-imbalanced model cannot enforce paramagnetic self-consistency and therefore at low temperature result in paramagnetic (PM) to antiferromagnetic (AFM) transition. In addition, in the PM state and at finite temperature, we observed a spin dependent crossover from Fermi liquid (FL) regime to non-Fermi liquid (nFL) regime in which the FL regime is destroyed, monotonically, induced not only by the interaction but also by the mass imbalance. We present the results for small cluster DCA and explore its dependency on cluster size as well.
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 investigate paramagnetic metal-insulator transitions in the infinite-dimensional ionic Hubbard model at finite temperatures. By means of the dynamical mean-field theory with an impurity solver of the continuous-time quantum Monte Carlo method, we show that an increase in the interaction strength brings about a crossover from a band insulating phase to a metallic one, followed by a first-order transition to a Mott insulating phase. The first-order transition turns into a crossover above a certain critical temperature, which becomes higher as the staggered lattice potential is increased. Further, analysis of the temperature dependence of the energy density discloses that the intermediate metallic phase is a Fermi liquid. It is also found that the metallic phase is stable against strong staggered potentials even at very low temperatures.
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.