Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles

We investigate the interplay of temperature and trap effects in cold particle systems at their quantum critical regime, such as cold bosonic atoms in optical lattices at the transitions between Mott-insulator and superfluid phases. The theoretical framework is provided by the one-dimensional Bose-Hubbard model in the presence of an external trapping potential, and the trap-size scaling theory describing the large trap-size behavior at a quantum critical point. We present numerical results for the low-temperature behavior of the particle density and the density-density correlation function at the Mott transitions, and within the gapless superfluid phase.