Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases

TL;DR

This paper explores the various insulating phases of spin-1 bosons in optical lattices, revealing how spin interactions lead to nematic, singlet, and dimerized phases with distinct symmetry properties and experimental signatures.

Contribution

It provides a comprehensive analysis of the phase diagram for spin-1 bosons in optical lattices, highlighting the conditions for nematic, singlet, and dimerized phases based on particle number and dimensionality.

Findings

Odd particle number per site leads to nematic or dimerized phases.

Even particle number per site results in a spin-singlet phase or a transition to nematic.

Experimental signatures include Bragg scattering and time-of-flight measurements.

Abstract

We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as Na-23, in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three- dimensional lattices insulating phases with odd number of particles per site are always nematic. For insulating states with even number of particles per site there is always a spin-singlet phase and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry, but preserves time reversal symmetry, and has gapless spin-wave excitations. The spin singlet phase does not break spin symmetry and has a gap to all excitations. In one-dimensional lattices insulating phases with odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.