arXiv:1212.6035 · Physical Review Letters

Ground States of the Spin-1 Bose-Hubbard Model

Hosho Katsura, Hal Tasaki

Published Mar 26, 2013• 29 citations

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 U2 of the spin-dependent interaction. We show that the ground state exhibits saturated ferromagnetism if U2<0, is spin-singlet if U2>0, and exhibits "SU(3)-ferromagnetism" if U2=0, and completely determine the degeneracy in each region.

DOI: 10.1103/physrevlett.110.130405

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arXiv:1212.6035 · Physical Review Letters

Ground States of the Spin-1 Bose-Hubbard Model

Hosho Katsura, Hal Tasaki

Published Mar 26, 2013• 29 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.110.130405

Related papers

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N_{\rm d}

-fold degenerate ground states. The degeneracy

N_{\rm d}

is proportional to the total number of sites $\absΛ$. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to $ρ_0=N_{\rm d}/(2\absΛ)$, and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.

We investigate the ground state of the Kondo-Hubbard model employing the recently introduced idea of spin-reflection positivity. It is shown exactly that the Kondo-Hubbard model for

J<0

and

U>|J|/4

at half filling has a unique ground state which can be ferromagnetic or singlet according to the lattice structure. In particular, for the Kondo lattice with

U>|J|/4

, the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling ${J}_{\ensuremath{\perp}}>0$ and ${J}_{z}\ensuremath{\le}0$ for

U>|{J}_{z}|/4

N=2n

(

n

is a positive integer) is unique for both models. For the second model, we show that the ground state has spin along the z-axis

S^{z}=0

. When the hopping coefficients are real, it has zero spin quantum number, i.e., it is a singlet. Our proofs work equally well for any arbitrary finite-size lattice.