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

TL;DR

This study uses variational Monte Carlo to explore how doublon-holon binding influences the Mott transition in two-dimensional Bose Hubbard models, proposing a new picture involving characteristic length scales.

Contribution

The paper introduces a novel framework with two length scales, $\xi_{ m dh}$ and $\xi_{ m dd}$, to better understand the Mott transition driven by doublon-holon binding.

Findings

Mott transition occurs when $\xi_{ m dh}$ is comparable to $\xi_{ m dd}$

D-H pairs overlap in the superfluid state, enabling independent propagation

Intersite repulsive factors are less significant for the transition

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