High-order symbolic strong-coupling expansion for the Bose-Hubbard model (A5)

Tao Wang, Xue-Feng Zhang, Chun-Feng Hou, Sebastian Eggert, and Axel Pelster:

Phys. Rev. B, 98, 245107 (2018)

🔓 arXiv:1801.01862 (2018)

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 Padé 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.