Strong-coupling expansion for the spin-1 Bose-Hubbard model

Abstract

In this study, we perform a strong-coupling expansion up to third order of the hopping parameter $t$ for the spin-1 Bose--Hubbard model with antiferromagnetic interaction. As expected from previous studies, the Mott insulator phase is considerably more stable against the superfluid phase when filling with an even number of bosons than when filling with an odd number of bosons. The phase-boundary curves are consistent with the perturbative mean-field theory in the limit of infinite dimensions. The critical value of the hopping parameter $t_{\mathrm{C}}$ at the peak of the Mott lobe depends on the antiferromagnetic interaction. This result indicates the reliability of the strong coupling expansion when $U_2$ possesses large (intermediate) values for Mott lobe with an even (odd) number of bosons. Moreover, in order to improve our results, we apply a few extrapolation methods up to infinite order in $t$. The fitting results of the phase-boundary curves agree better with those of the perturbative mean-field approximation. In addition, the linear fit error of $t_{\mathrm{C}}$ is very small for the strong antiferromagnetic interaction.

22 pages, 11 figures

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• Mott Transition and Spin Structures of Spin-1 Bosons in Two-Dimensional Optical Lattice at Unit Filling

Cited by in corpus (10)

• Ultracold bosons with short-range interaction in regular optical lattices
• Interacting spin-1 bosons in a two-dimensional optical lattice
• Magnetic phases of spin-1 lattice gases with random interactions
• Phase Diagrams of Antiferromagnetic Spin-1 Bosons on Square Optical Lattice with the Quadratic Zeeman Effect
• Phase transitions and spin excitations of spin-1 bosons in optical lattice
• Quantum phases of a spin-1 ultracold Bose gas with three body interactions
• Spin-1 Bose-Hubbard model with two- and three-body interactions
• Strong-coupling study of spin-1 bosons in square and triangular optical lattice
• Spinor bosons in optical superlattices: a numerical study
• Effects of an attractive three body interaction on a spin-1 Bose Hubbard model