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arXiv:2309.03915

Nearest-Neighbor Tunneling Ansatz in the Bose-Hubbard Mode

Moorad Alexanian

Published Sep 4, 2023• 0 citations
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Abstract

A recently introduced recurrence-relation ansatz applied to the Jaynes-Cummings-Hubbard model is here applied to the Bose-Hubbard model that reduced the model to an easily soluble model. The results obtained for the two-point density correlations resemble somewhat those obtained recently also but in a much more complicated fashion. Our ansatz may be of value for the solution of many-body quantum mechanical problems.

DOI
10.48550/arxiv.2309.03915

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Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.
We propose a realization of an extended Bose-Hubbard model, which takes into account next-nearest-neighbor tunneling, by one-dimensional double-well optical superlattice with a resonance between s and p orbitals in the neighboring sites. Custom method of finding maximally-localized Wannier functions enables us to compute physical tunneling coefficients, which put some restrictions on the studies of the model, what have recently been done using arbitrary values of parameters. Furthermore, it turns out that out of s-p resonance the system splits up into two disconnected lattices. We analyze also Zak-Berry phase and single-particle spectrum of the system. In order to present the problem in the full context, short review of rudiments of optical lattice physics and derivation of the standard Bose-Hubbard model is included.