Ground States of the Spin-1 Bose-Hubbard Model

TL;DR

This paper rigorously characterizes the ground states of the spin-1 Bose-Hubbard model, revealing universal magnetic phases depending solely on the spin-dependent interaction coefficient U_2.

Contribution

It provides the first rigorous theorems classifying ground states of the spin-1 Bose-Hubbard model based on U_2, including ferromagnetic, spin-singlet, and SU(3)-ferromagnetic phases.

Findings

Ground state is saturated ferromagnetism if U_2<0.

Ground state is spin-singlet if U_2>0.

Ground state exhibits SU(3)-ferromagnetism at U_2=0.

Abstract

We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U_2 of the spin-dependent interaction. We show that the ground state exhibits saturated ferromagnetism if U_2<0, is spin-singlet if U_2>0, and exhibits "SU(3)-ferromagnetism" if U_2=0, and completely determine the degeneracy in each region.