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Communications in Theoretical Physics

Factorizable S Matrices and Symmetry Operators

Zhan-Ning Hu

Published Dec 15, 1994• 0 citations
Publisher

Abstract

In this paper, the factorizable S matrices with toroidal rapidity values are constructed explicitly and the symmetry operators of which tensor product commutes with S are found. These operators have a structure which is similar to the ordinary Hopf algebra. As a limit of the elliptic case sl q (2) quantum algebra with q N = 1 can be obtained from the symmetry operators.

DOI
10.1088/0253-6102/22/4/425

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In this paper, the factorizable S matrices with toroidal rapidity values are constructed explicitly and the symmetry operators of which tensor product commutes with S are found. These operators have a structure which is similar to the ordinary Hopf algebra. As a limit of the elliptic case sl q (2) quantum algebra with q N = 1 can be obtained from the symmetry operators.
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We develop an approach for constructing the Baxter -operators for generic sl ( N ) spin chains. The key element of our approach is the possibility of representing a solution of the Yang–Baxter equation in the factorized form. We prove that such a representation holds for a generic sl ( N ) invariant -operator and find the explicit expression for the factorizing operators. Taking trace of monodromy matrices constructed of the factorizing operators one defines a family of commuting (Baxter) operators on the quantum space of the model. We show that a generic transfer matrix factorizes into the product of N Baxter -operators and discuss an application of this representation for a derivation of functional relations for transfer matrices.
We have constructed series of the spectral parameter dependent solutions to the Yang–Baxter equations defined on the tensor product of reducible representations with a symmetry of quantum (super)algebra. These series are produced as descendant solutions from the s l q ( 2 ) -invariant Hecke type R r r ( u ) -matrices. The analogues of the matrices of Hecke type with the symmetry of the quantum super-algebra o s p q ( 1 | 2 ) are obtained precisely. For the homogeneous solutions R r 2 − 1 r 2 − 1 there are constructed Hamiltonian operators of the corresponding one-dimensional quantum integrable models, which describe rather intricate interactions between different kind of spin states. Centralizer operators defined on the products of the composite states are discussed. The inhomogeneous series of the operators R r R ( u ) , extended Lax operators of Hecke type, also are suggested.