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High-order symbolic strong-coupling expansion for the Bose-Hubbard model
Combining the process-chain method with a symbolized evaluation we work out
in detail a high-order symbolic strong-coupling expansion (HSSCE) for
determining the quantum phase boundaries between the Mott insulator and the
superfluid phase of the Bose-Hubbard model for different fillings in hypercubic
lattices of different dimensions. With a subsequent Pad{\'e} approximation we
achieve for the quantum phase boundaries a high accuracy, which is comparable
to high-precision quantum Monte-Carlo simulations, and show that all the Mott
lobes can be rescaled to a single one. As a further cross-check, we find that
the HSSCE results coincide with a hopping expansion of the quantum phase
boundaries, which follow from the effective potential Landau theory (EPLT).Comment: 15 pages, 11 figures. For the latest version and more information see
https://www.physik.uni-kl.de/eggert/papers/index.htm
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