Communications in Theoretical Physics

Colored Quantum Algebra and Its Bethe State

Jin-Zheng Wang, Xiao-Yu Jia, Shikun Wang

Published Dec 1, 2014• 0 citations

Abstract

We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.

DOI: 10.1088/0253-6102/62/6/01

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Communications in Theoretical Physics

Colored Quantum Algebra and Its Bethe State

Jin-Zheng Wang, Xiao-Yu Jia, Shikun Wang

Published Dec 1, 2014• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/62/6/01

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We construct

R

-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They change with the representation of the latter. The associated Yang-Baxter algebra and the spectrum of the transfer matrix are also studied.

q

is a root of unity. We start by solving the six-vertex model with fixed boundary conditions (FBC) that guarantee exact

SU(2)_q

invariance on the lattice. The algebra of the Yang-Baxter (YB) and

SU(2)_q

generators turns to close. The infinite spectral parameter limit of the YB generators yields {\bf cleanly} the

SU(2)_q

generators. The Bethe Ansatz states constructed for FBC are shown to be {\bf highest weights} of

SU(2)_q

. The higher level Bethe Ansatz equations (BAE, describing the physical excitations) are explicitly derived for FBC. We then solve the RSOS(

p

) models on the light--cone lattice with fixed boundary conditions by disentangling the type II representations of

SU(2)_q

, at

q=e^{iπ/p}

, from the full SOS spectrum obtained through Algebraic Bethe Ansatz. The RSOS states are those with quantum spin $J