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Journal Article

High-order symbolic strong-coupling expansion for the Bose-Hubbard model


Zhang,  Xue-Feng
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Wang, T., Zhang, X.-F., Hou, C.-F., Eggert, S., & Pelster, A. (2018). High-order symbolic strong-coupling expansion for the Bose-Hubbard model. Physical Review B, 98(24): 245107. doi:10.1103/PhysRevB.98.245107.

Cite as: http://hdl.handle.net/21.11116/0000-0002-BD9F-7
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 Pade 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.