Vortex-Lattice Phases in the Strongly-Interacting Limit of the Bose-Hubbard Model

Mukesh Khanore, Bishwajyoti Dey

Masahito Ueda, Hiroki Saito

T. H. Johnson, Yongjun Yuan, Weizhu Bao +3 more

We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.

Sagarika Basak, Han Pu

Sergei V. Isakov, K. Sengupta, Yong Baek Kim

We analyze the Bose-Hubbard model of hardcore bosons with nearest-neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong-interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second-order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.

K. Sengupta, N. Dupuis

We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.