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Chinese Physics B

Quantum phase transitions of fermionic atoms in an anisotropic triangular optical lattice

An Bao, Yao‐Hua Chen, Xiaozhong Zhang

Published Nov 1, 2013• 5 citations
Publisher

Abstract

The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte—Carlo algorithm. The quantum phase diagrams which reflect the temperature—interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system. Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value. The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect. A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed, in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.

DOI
10.1088/1674-1056/22/11/110309

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The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte—Carlo algorithm. The quantum phase diagrams which reflect the temperature—interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system. Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value. The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect. A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed, in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.
Quantum phase transition of fermionic atoms in anisotropic triangular optical lattice was investigated by dynamical cluster approximation combining with continuous time quantum Monte Carlo algorithm. The temperature-interaction phase diagram for different hoping terms and the competition between the anisotropic parameter and interaction is presented. Our results show that the system undergoes Mott transition from Fermi liquid to Mott insulator while the repulsive interaction reach the critical value. The Kondo metal characterized by Kondo peak in the density of states is found in this systems and the pseudogap are suppressed at low temperature due to the Kondo effect. We also propose a feasible experiment protocol to observe these phenomenon in the anisotropic triangular optical lattice with the cold atoms, in which the hoping terms can be varied by the lattice depth and the atomic interaction can be adjusted via Feshbach resonance.
We investigate the strongly correlated effect of cold atoms in triangular optical lattice by dynamical cluster approximation combining with the continuous time quantum Monte Carlo method proposed recently. It is found the double occupancy is suppressed as the atomic interaction increases. By calculating the density of states, we show how the system evolves from Fermi liquid with an obvious quasi-particle peak into Mott insulator with an opened gap for increasing interaction. The transition between Fermi liquid and pseudogap shows a reentrant behavior due to the Kondo effect. At low temperature, a Kondo peak appears before the splitting of the Fermi-liquid-like peak. The Fermi surface evolves from a circular ring with high amplitude into a °at elliptical ring with low amplitude for the increasing interaction. We give an experimental protocol to observe these phenomena by varying the lattice depth and the atomic interaction via Feshbach resonance in future experiments.
We investigate the strongly correlated effect of cold atoms in a triangular optical lattice using the dynamical cluster approximation combined with the continuous-time quantum Monte Carlo method. When the interaction increases, the Fermi surface evolves from a circular ring into a flat plane, and the system transitions from a Fermi liquid into a Mott insulator. The transition between the Fermi liquid and a pseudogap shows a reentrant behavior due to the Kondo effect. We give an experimental protocol to observe these phenomena in future experiments by varying the lattice depth and the atomic interaction via the Feshbach resonance.
We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.
We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal–insulator transition increases for fixed temperature. The interaction–anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.
In this work, the Hubbard model is adopted to describe fermions with on-site repulsive interaction and the nearest-neighbor hopping in anisotropic ruby lattice. The combination of cluster dynamical mean field theory and continuous-time quantum Monte Carlo algorithm is used to solve the theoretical model. It is widely accepted that the density of states and the double occupancy are two important quantities for determining the phase transition of two-dimensional strongly correlated system. Therefore, based on the self-consistent calculation, using the maximum entropy method to calculate the single particle density of states and double occupancy of fermions in anisotropic ruby lattice. Here in this work, there are 6 sites in a cluster. The influences of temperature, interaction and anisotropic parameter on metal-insulator phase transition of fermions in anisotropic ruby lattice are discussed based on the calculations of single particle density of state and double occupancy. Finally, the metal-Mott insulator phase diagram which shows the competition between temperature and on-site repulsive interaction in the phase transition of fermions in anisotropic ruby lattice is presented. The results shows that the system is in metallic state for the regime of weak interaction and low temperature, and the Mott insulator appears in the regime of strong interaction and high temperature. The metallic state and Mott insulating one are separated by the second-order transition line in the phase diagram.