Calculation of the n=1 Critical Point in the Bose-Hubbard Model on the Isotropic Union Jack Lattice via Quantum Monte Carlo (QMC)

Keywords: Bose--Hubbard model, Union Jack lattice, Quantum Monte Carlo

Abstract: This paper presents a detailed computation of the critical point $\frac{t}{U}_c$ for the superfluid-Mott insulator transition at unit filling (n=1) in the Bose-Hubbard model on the isotropic Union Jack lattice. Employing quantum Monte Carlo techniques, specifically the stochastic series expansion (SSE) directed-loop algorithm, we tune the chemical potential to enforce unit density and use finite-size scaling of winding numbers to extrapolate the thermodynamic-limit critical value. The Hamiltonian, lattice structure, algorithmic implementations, methodological critiques, and final numerical result of $\frac{t}{U}_c = 0.02992 \pm 0.00020 $ are discussed, preserving all key formulas and logical derivations.

Submission Number: 298