Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains

Details Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains

2008-09-11

arxiv.org/abs/0809.2050v2

J.Phys.A42:075204,2009

Nonlinear Sciences

Exactly Solvable and Integrable Systems

41 pages, 5 figures, published version

Scientific paper

10.1088/1751-8113/42/7/075204

We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that such a representation holds for a generic sl(N) invariant R-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 Q-operators and discuss an application of this representation for a derivation of functional relations for transfer matrices.

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