Abstract
We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as {sup 23}Na, 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 an odd number of particles per site are always nematic. For insulating states with an 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 an 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.
Highlights
Modern studies of quantum magnetism in condensed matter physics go beyond explaining details of particular experiments on cuprate superconductors, heavy fermion materials, organic conductors, or related materials, and aim to develop general paradigms for understanding complex orders in strongly interacting many-body systems1–10͔
The situation may change dramatically when either the atomic scattering length is changed by means of Feshbach resonance12͔ or when an optical potential created by standing laser beams confines particles in the minima of the periodic potential and strongly enhances the effects of interactions
VI we summarize our results and review the global phase diagram for spin-1 bosons in optical lattices
Summary
Modern studies of quantum magnetism in condensed matter physics go beyond explaining details of particular experiments on cuprate superconductors, heavy fermion materials, organic conductors, or related materials, and aim to develop general paradigms for understanding complex orders in strongly interacting many-body systems1–10͔. The situation may change dramatically when either the atomic scattering length is changed by means of Feshbach resonance12͔ or when an optical potential created by standing laser beams confines particles in the minima of the periodic potential and strongly enhances the effects of interactions In the latter case, the existence of the nontrivial Mott insulating state of atoms in optical lattices, separated from the superfluid phase by the quantum phase transitionSI transition, was demonstrated recently in experiments13–15͔. III we derive an effective spin Hamiltonian which is valid for any odd number of atoms per site N
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
