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

Abstract

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 ${\xi }_{\mathrm{dh}}$ and the minimum D-D exclusion length ${\xi }_{\mathrm{dd}}$. Generally, a Mott transition occurs when ${\xi }_{\mathrm{dh}}$ becomes comparable to ${\xi }_{\mathrm{dd}}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other (${\xi }_{\mathrm{dh}}>{\xi }_{\mathrm{dd}}$); 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.

16 pages, 22 figures, submitted to J. Phys. Soc. Jpn

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