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Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $ξ_{\rm dh}$ and the minimum D-D exclusion length $ξ_{\rm dd}$. Generally, a Mott transition occurs when $ξ_{\rm dh}$ becomes comparable to $ξ_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($ξ_{\rm dh}>ξ_{\rm dd}$); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.