Hannover 2013 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 40: Quantum gases: Optical lattices II

Q 40.2: Talk

Wednesday, March 20, 2013, 14:15–14:30, A 310

Mean-field theory for extended Bose-Hubbard model with hard-core bosons — •Mathias May¹, Nicolas Gheeraert², Shai Chester³, Sebastian Eggert⁴, and Axel Pelster⁴ — ¹Institut für Theoretische Physik, Freie Universität Berlin, Germany — ²Institute of Theoretical Physics, University of Edinburgh, UK — ³Physics Department, Columbia University, USA — ⁴Fachbereich Physik, Technische Universität Kaiserslautern, Germany

We solve the extended Bose-Hubbard Model with hard-core bosons within mean-field theory for both a quadratic and a triangular lattice. To this end the nearest neighbor terms involving both interaction and hopping are factorized into a mean field and an operator. Assuming additionally a natural division of the lattice into sublattices, we yield a much simpler two- or three-site mean-field Hamiltonian for the quadratic and triangular lattice, respectively. Considering an on-site hard-core interaction allows each site to be occupied by at most one boson, thus the two- or three-site mean-field Hamiltonian reduces to a 4x4- or 8x8-matrix. The resulting energy eigenvalues have to be extremized with respect to the order parameters, which represent the condensate density and the average number of particles for each of the sublattices. As a result we obtain a mean-field phase diagram, which consists of a Mott insulator phase, a density wave phase, a superfluid phase and, for the triangular lattice, also of a supersolid phase. Finally, we determine whether the respective transition lines in the phase diagram are of first or second order and compare our results with recent quantum Monte Carlo simulations.