Momentum distribution of noncondensate particles near the superfluid-to-Mott-insulator transition of bosonic atoms in a uniform optical lattice

We investigate the finite temperature momentum distribution of bosonic noncondensate particles inside a uniform three-dimensional optical lattice near the superfluid-to-Mott-insulator transition point, treating quantum fluctuations and thermal fluctuations on equal footing. We explicitly address the different momentum (q) dependences of quasiparticle distribution resulted from thermal and quantum origins: the former scales as vertical bar q vertical bar(-2) and hence is dominant in the small momentum region, while the later scales as vertical bar q vertical bar(-1) and hence is dominant in the large momentum limit. Semianalytical results are derived and therefore can be applied to a further study of strongly interacting bosonic systems. Our results also agree with the scaling theory of a quantum XY model near the transition point.