arXiv:cond-mat/9902269 · Physical review. B, Condensed matter

Ground state and excitations of a spin chain with orbital degeneracy

You‐Quan Li, Michael Ma, Daning Shi, Fu‐Chun Zhang

Published Nov 1, 1999• 40 citations

Abstract

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the $\mathrm{SU}(4)$ symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a $\mathrm{SU}(4)$ singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

DOI: 10.1103/physrevb.60.12781

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arXiv:cond-mat/9902269 · Physical review. B, Condensed matter

Ground state and excitations of a spin chain with orbital degeneracy

You‐Quan Li, Michael Ma, Daning Shi, Fu‐Chun Zhang

Published Nov 1, 1999• 40 citations

arXiv HTML PDF

Abstract

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the

\mathrm{SU}(4)

symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a

\mathrm{SU}(4)

singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

DOI: 10.1103/physrevb.60.12781

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Jan 1, 19956 citations

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the

\mathrm{SU}(4)

\mathrm{SU}(4)

A spin-

\frac{1}{2}

system with double orbital degeneracy may possess SU(4) symmetry. According to the group theory a global SU(4) singlet state can be expressed as a linear combination of all possible configurations consisting of four-site SU(4) singlets. Following Andersion's idea for spin-

\frac{1}{2}

system, we propose that the ground state for the antiferromagnetic SU(4) model is an SU(4)-resonating valence-bond (RVB) state. A short-range SU(4)-RVB state is a spin and orbital liquid, and its elementary excitations has an energy gap. We construct a series of solvable models that ground states are short-range SU(4)-RVB states. The results are generalized to the antiferromagnetic SU(N) models.

N

number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving Bethe-ansatz equation numerically. For infinite

N,

the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit.

The Hubbard model for electrons with orbital degeneracy is shown to have an underlying

{\mathrm{SU}}_{d}(4)

symmetry of spin-orbital double. A hidden charge

{\mathrm{SU}}_{c}(4)

symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a

\mathrm{SO}(6)

Heisenberg magnet at half-filling and a

\mathrm{SU}(4)

one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.

An anisotropic integrable spin chain, consisting of spins

s=1

and

s=\frac{1}{2}

, is investigated \cite{devega}. It is characterized by two real parameters

\bar{c}

and

\tilde{c}

, the coupling constants of the spin interactions. For the case

\bar{c}<0

and

\tilde{c}<0

the ground state configuration is obtained by means of thermodynamic Bethe ansatz. Furthermore the low excitations are calculated. It turns out, that apart from free magnon states being the holes in the ground state rapidity distribution, there exist bound states given by special string solutions of Bethe ansatz equations (BAE) in analogy to \cite{babelon}. The dispersion law of these excitations is calculated numerically.