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Physical Review A

Cold atoms in a two-dimensional triangular optical lattice as an artificial frustrated system

Yao‐Hua Chen, Wéi Wú, Hong-Shuai Tao, Wu-Ming Liu

Published Oct 26, 2010• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.82.043625

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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 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.
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.
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.
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.
The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous-time auxiliary-field quantum Monte Carlo to solve this model for 1-, 4-, 6-, 12-, and 16-site clusters with detailed analysis performed for the 6-site cluster. We show that (a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; (b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; and (c) the loss of spectral weight in the metal-to-Mott-insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.
We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.