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

Abstract

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{é} 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).

15 pages, 11 figures. For the latest version and more information see https://www.physik.uni-kl.de/eggert/papers/index.html

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Cited by in corpus (8)

• Beyond hard-core bosons in transmon arrays
• Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory
• Quantum phase transition of the two-dimensional Rydberg atom array in an optical cavity
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Emergence of damped-localized excitations of the Mott state due to disorder
• Two-body contact of a Bose gas near the superfluid--Mott-insulator transition
• Quantum phase transition of the Bose-Hubbard model on cubic lattice with anisotropic hopping
• Simplifying higher-order perturbation theory for ring-shaped Bose-Hubbard systems