Numerical study of 1-D and lattice Bose gases at finite temperature
combining stochastic simulations and DMRG

Lev Plimak

FB Physik, AG Theoretische Quantenoptik, Technische Universität Kaiserslautern,
Erwin-Schrödinger Strasse 46, 67663 Kaiserslautern, Germany

Using the Bose Hubbard model as a generic model for Bosons in a lattice (discretized 1-D trap), we discuss a numerical approach combining Monte-Carlo techniques based on stochastic factorisation of hopping (respectively, discretized kinetic energy) with concepts originating in the Density Matrix Renormalisation Group (DMRG). Numerical results for a trapped 1D Bose gas in the Tonks, the Gross-Pitaevskii, and the intermediate regimes are presented, as well as numerical studies of finite-temperature effects on number fluctuations in a one dimensional lattice gas. We then show that important characteristics of the lattice gas may also be obtained in a simple perturbative approach.