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

TL;DR

This paper develops a high-order symbolic strong-coupling expansion method for accurately determining the phase boundaries in the Bose-Hubbard model, matching results from quantum Monte-Carlo simulations.

Contribution

It introduces a novel high-order symbolic expansion combined with Padé approximation for precise phase boundary calculations in the Bose-Hubbard model.

Findings

High accuracy in phase boundary determination comparable to quantum Monte-Carlo.

All Mott lobes can be rescaled to a single universal form.

Results agree with effective potential Landau theory predictions.

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{\'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).