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arXiv:1201.2068 · Physical Review B

Orbital-selective crossover and Mott transitions in an asymmetric Hubbard model of cold atoms in optical lattices

Emilio A. Winograd, R. Chitra, Marcelo J. Rozenberg

Published Dec 8, 2011• 14 citations
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Abstract

We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.

DOI
10.1103/physrevb.84.233102

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We study the asymmetric Hubbard model at half filling as a generic model to describe the physics of two species of repulsively interacting fermionic cold atoms in optical lattices. We use dynamical mean-field theory to obtain the paramagnetic phase diagram of the model as a function of temperature, interaction strength, and hopping asymmetry. A Mott transition with a region of two coexistent solutions is found for all nonzero values of the hopping asymmetry. At low temperatures the metallic phase is a heavy Fermi liquid, qualitatively analogous to the Fermi-liquid state of the symmetric Hubbard model. Above a coherence temperature, an orbital-selective crossover takes place, wherein one fermionic species effectively localizes, and the resulting bad metallic state resembles the non-Fermi-liquid state of the Falicov-Kimball model. We compute observables relevant to cold atom systems such as the double occupation, the specific heat, and entropy, and characterize their behavior in the different phases.
We study the phase diagram of the asymmetric Hubbard model (AHM), which is characterized by different values of the hopping for the two spin projections of a fermion or, equivalently, two different orbitals. This model is expected to provide a good description of a mass-imbalanced cold fermionic mixture in a 3D optical lattice. We use the dynamical mean-field theory to study various physical properties of this system. In particular, we show how orbital-selective physics, observed in multiorbital strongly correlated electron systems, can be realized in such a simple model. We find that the density distribution is a good probe of this orbital-selective crossover from a Fermi-liquid to a non-Fermi-liquid state. Below an ordering temperature To{T}_{o}To​, which is a function of both the interaction and hopping asymmetry, the system exhibits staggered long-range orbital order. Apart from the special case of the symmetric limit, i.e., Hubbard model, where there is no hopping asymmetry, this orbital order is accompanied by a true charge density wave order for all values of the hopping asymmetry. We calculate the order parameters and various physical quantities including the thermodynamics in both the ordered and disordered phases. We find that the formation of the charge density wave is signaled by an abrupt increase in the sublattice double occupancies. Finally, we propose a new method, entropic chromatography, for cooling fermionic atoms in optical lattices, by exploiting the properties of the AHM. To establish this cooling strategy on a firmer basis, we also discuss the variations in temperature induced by the adiabatic tuning of interactions and hopping parameters.
We investigate the Mott metal-insulator transition in the asymmetric Hubbard model, which may describe the ground states of fermionic atoms trapped in optical lattices. We use the dynamical mean-field theory and the equation of motion approach to calculate the density of states at the Fermi level and the double occupation for various values of the on-site interaction U and the hopping asymmetry r . The critical interaction is also obtained as a function of the hopping asymmetry. Our results are in good agreement with the ones obtained by using the dynamical mean field theory with the exact diagonalization and the quantum Monte Carlo techniques.
The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction (TTT-UUU) plane. With increasing UUU, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing UUU. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.
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 two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the magnetically ordered and superfluid states are not realized, but the metal-insulator transition occurs. This transition is characterized by the Mott and pairing transitions discussed in the conventional repulsive and attractive Hubbard models. In the doped system, commensurability emerges owing to the repulsive interactions and the metal-insulator transition occurs down to quarter-filling.
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.