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 the case of no magnetic influence, superfluid-insulator (Mott) transitions in the S = 0 Bose Hubbard model at unit filling are studied on 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 ζ_dh and the minimum D-D exclusion length ζ_dd. Generally, a Mott transition occurs when ζ_dh becomes comparable to ζ_dd. In the conductive (superfluid) state, domains of D-H pairs overlap with each other (ζ_dh > ζ_dd); therefore, D and H can propagate independently as density carriers by successively exchanging partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.