Using large-scale quantum Monte Carlo simulations we study bosons hopping on a triangular lattice with nearest $(V)$ and next-nearest $({V}^{\ensuremath{'}})$ neighbor repulsive interactions. In the limit where $V=0$ but ${V}^{\ensuremath{'}}$ is large, we find an example of an unusual period-three striped supersolid state that is stable at $1∕2$ -filling. We discuss the relationship of this state to others on the rich ground-state phase diagram, which include a previously discovered supersolid, a uniform superfluid, as well as several Mott insulating phases. We study several superfluid- and supersolid-to-Mott phase transitions, including one proposed by a recent phenomenological dual vortex field theory as a candidate for an exotic deconfined quantum critical point. We find no examples of unconventional quantum criticality among any of the interesting phase transitions in the model.Using large-scale quantum Monte Carlo simulations we study bosons hopping on a triangular lattice with nearest $(V)$ and next-nearest $({V}^{\ensuremath{'}})$ neighbor repulsive interactions. In the limit where $V=0$ but ${V}^{\ensuremath{'}}$ is large, we find an example of an unusual period-three striped supersolid state that is stable at $1∕2$-filling. We discuss the relationship of this state to others on the rich ground-state phase diagram, which include a previously discovered supersolid, a uniform superfluid, as well as several Mott insulating phases. We study several superfluid- and supersolid-to-Mott phase transitions, including one proposed by a recent phenomenological dual vortex field theory as a candidate for an exotic deconfined quantum critical point. We find no examples of unconventional quantum criticality among any of the interesting phase transitions in the model.

arXiv:cond-mat/0607501Physical Review BDec 26, 200633 citations

Supersolid phases for lattice bosons: a variational calculation

R. Baltin, Karl-Heinz Wagenblast, Gerd Schön +1 more

Jan 1, 19950 citations

Diverse solid and supersolid phases of bosons in a triangular lattice

Qi-Hui Chen, Peng Li

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.

Chinese Physics BMay 1, 20145 citations

Supersolidity of cold-atom Bose-Fermi mixtures in optical lattices

Peter P. Orth, Doron L. Bergman, Karyn Le Hur

We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of ${n}_{f}=3∕4$ with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of $^{87}\mathrm{Rb}^{40}\mathrm{K}$ and $^{23}\mathrm{Na}^{6}\mathrm{Li}$ , we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of ${n}_{f}=3∕4$ with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of $^{87}\mathrm{Rb}^{40}\mathrm{K}$ and $^{23}\mathrm{Na}^{6}\mathrm{Li}$, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.

arXiv:0905.1125Physical Review AAug 28, 200936 citations

Using large-scale quantum Monte Carlo simulations we study bosons hopping on a triangular lattice with nearest

(V)

and next-nearest $({V}^{\ensuremath{'}})$ neighbor repulsive interactions. In the limit where

V=0

but ${V}^{\ensuremath{'}}$ is large, we find an example of an unusual period-three striped supersolid state that is stable at

1∕2

-filling. We discuss the relationship of this state to others on the rich ground-state phase diagram, which include a previously discovered supersolid, a uniform superfluid, as well as several Mott insulating phases. We study several superfluid- and supersolid-to-Mott phase transitions, including one proposed by a recent phenomenological dual vortex field theory as a candidate for an exotic deconfined quantum critical point. We find no examples of unconventional quantum criticality among any of the interesting phase transitions in the model.

{n}_{f}=3∕4

with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of

^{87}\mathrm{Rb}^{40}\mathrm{K}

and

^{23}\mathrm{Na}^{6}\mathrm{Li}

, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.