Spin and quadruple correlations in the insulating nematic phase of spin-1 bosons on optical lattices

TL;DR

This paper investigates the spin and quadrupole correlations in the insulating nematic phase of spin-1 bosons on optical lattices, revealing phase transitions and dominant fluctuation patterns in 1D and 2D systems.

Contribution

It introduces a valence bond mean field theory for the effective model and identifies a first-order phase transition in 1D and nematic order in 2D.

Findings

First-order transition from spin singlet to nematic phase in 1D at J1/J2=0.19833

Nematic ordered phase with gapless excitations in 2D square lattice

Dominant antiferromagnetic and ferroquadrupolar correlations in both dimensions

Abstract

We consider the effective model of $H=-J_{1}\sum_{<i,j>}\mathbf{S}_{i}\cdot \mathbf{S}_{j}-J_{2}\sum_{<i,j>}(\mathbf{S}_{i}\cdot \mathbf{S}_{j}) ^{2}$, describing the Mott insulating phase with odd number of spin-1 bosons in optical lattices ($J_{2}>J_{1}>0$). In terms of an SU(3) boson representation, a valence bond mean field theory is developed. In 1D, a \textit{first-order} quantum phase transition from a spin singlet to a spin nematic phase with \textit{gapful} excitations is identified at $ J_{1}/J_{2}=0.19833$, while on a 2D square lattice a spin nematic ordered phase with gapless excitations prevails. In both 1D and 2D cases, we predict that the spin structure factor displays dominant antiferromagnetic fluctuations, while the quadrupole structure factor exhibits strong ferroquadrupolar correlations.