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We study the momentum resolved single particle spectrum and the dynamic structure factor of several versions of the Bose Hubbard model in 1 and 2 dimensions using Quantum Monte Carlo, with comparison to recent analytical work. We investigate both the Mott phase and the superfluid phase. A model of coupled cavities containing single two-level systems, and communicating by bosons ("solid light") is investigated in 1d and shown to exhibit very similar spectral properties, even though it does not contain any explicit repulsion.
In 1d, we also investigate the Bose Hubbard model in a trap, corresponding to experiments in optical lattices, which have recently gained the ability to access spectral information. In 2d, we study the model at zero and at finite temperature, and show that the dynamic structure factor in the Mott region is very sensitive to temperature, exhibiting new low energy excitations at large temperature. The phase transition from the superfluid phase at low temperature to a normal fluid at large T is sensitively traced no only by the superfluid weight, but also by the spectral width of the dynamic structure factor at momentum (pi,pi), which thus provides another instrument to gauge temperature. |
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