Mott Transition and Spin Structures of Spin-1 Bosons in Two-Dimensional Optical Lattice at Unit Filling

TL;DR

This study investigates the ground state phases of spin-1 bosons in a 2D optical lattice at unit filling, revealing how spin interactions influence superfluid-Mott transitions and magnetic orderings.

Contribution

It introduces a variational Monte Carlo approach with a doublon-holon binding factor to effectively capture inter-site correlations in the S=1 Bose-Hubbard model.

Findings

Spin-dependent interactions alter the superfluid-Mott transition.

Nematic order emerges for antiferromagnetic coupling.

Ferromagnetic order appears for ferromagnetic coupling.

Abstract

We study the ground state properties of spin-1 bosons in a two-dimensional optical lattice, by applying a variational Monte Carlo method to the S=1 Bose-Hubbard model on a square lattice at unit filling. A doublon-holon binding factor introduced in the trial state provides a noticeable improvement in the variational energy over the conventional Gutzwiller wave function and allows us to deal effectively with the inter-site correlations of particle densities and spins. We systematically show how spin-dependent interactions modify the superfluid-Mott insulator transitions in the S=1 Bose-Hubbard model due to the interplay between the density and spin fluctuations of bosons. Furthermore, regarding the magnetic phases in the Mott region, the calculated spin structure factor elucidates the emergence of nematic and ferromagnetic spin orders for antiferromagnetic ($U_2>0$) and ferromagnetic ($U_2<0$) couplings, respectively.