Quantum rotor description of the bosonic superfluid—Mott insulator transition in optical lattices

摘要

The physics of the Bose–Hubbard (BH) model is the subjectof intensive studies in recent years, since it has been realizedthat BH Hamiltonian can be applied to systems of cold atomsconfined in periodic, optical lattice potential, where the effectson interactions are strongly enhanced. Our aim is to extend thewidely used mean-field treatment of the superfluid–Mott insu-lator (SF-MI) transition in the BH model. Our method also im-proves the strong-coupling expansion that works well, only forsufficiently large insulating gap. The key point of the approachis to consider the representation of strongly interacting bosonsas particles with attached U(1) gauge group flux tubes, which constitutes the quantum rotor description The effective actionformalism allows us to cast the problem in terms of the phase-only action and obtain an analytical formulas for critical lines.Finally, we calculate the zero-temperature SF—MI phase dia-grams for three-dimensional BH model and compare our re-sults with the outcome of numerical Monte Carlo simulations.We found a very good agreement for the quantitative results re-garding the details a the lobe in the phase diagrams showingthe quantum transition from superfluid to the Mott insulatingphase.