Renormalization-group analysis of p-orbital Bose-Einstein condensates in a square optical lattice

We investigate the quantum fluctuation effects in the vicinity of the critical point of a p-orbital bosonic system in a square optical lattice using the Wilsonian renormalization group, where the p-orbital bosons condense at nonzero momenta and display rich phases including both time-reversal symmetry invariant and broken Bose-Einstein condensation states. The one-loop renormalization-group analysis generates corrections to the mean-field phase boundaries. We also show the quantum fluctuations in the p-orbital system tend to induce the ordered phase but not destroy it via the Coleman-Weinberg mechanism, which is qualitatively different from the ordinary quantum fluctuation corrections to the mean-field phase boundaries in s-orbital systems. Finally, we discuss the observation of these phenomena in the realistic experiment.