We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing \mathrm{U}\left(1\right) quantum rotor approach and the topologically constrained path integral that includes a summation over \mathrm{U}\left(1\right) topological charge. We derive an effective quantum action for the BH model, which enables a non-perturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f=0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.
Chiral phases and dynamics of dipoles in triangular optical ladders
Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Jagiellonian University in Krakow（克拉科夫雅盖隆大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow（克拉科夫雅盖隆大学马克·卡克复杂系统研究中心）
Chiral and pair superfluidity in triangular ladder produced by state-dependent Kronig-Penney lattice
Institute of Theoretical Physics and Astronomy, Faculty of Physics, Vilnius University（维尔纽斯大学物理学院理论物理与天体物理研究所）；Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学量子系统单元）
