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Motivated by the recent experiment on p-orbital band bosons in opticallattices, we study theoretically the quantum phases of Mott insulator andsuperfluidity in two-dimensions. The system features a novel superfluid phasewith transversely staggered orbital current at weak interaction, and a Mottinsulator phase with antiferro-orbital order at strong coupling andcommensurate filling. We go beyond mean field theory and derive from amicroscopic model an effective action that is capable of describing both thep-band Mott insulating and superfluid phases in strong coupling. We furthercalculate the excitation spectra near the quantum critical point and find twogapless modes away from the tip of the Mott lobe but four gapless modes at thetip. Our effective theory reveals how the phase coherence peak builds up in theMott regime when approaching the critical point. We also discuss the finitetemperature phase transition of p-band superfluidity.

Effective action approach to the p-band Mott insulator and superfluid transition