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

Abstract

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.

41 pages, 5 figures, published version

References in corpus (24)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• Baxter's Q-operator for the homogeneous XXX spin chain
• Multi-loop Feynman integrals and conformal quantum mechanics
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Separation of variables for the quantum SL(2,R) spin chain
• Quantum Group Representations and Baxter Equation
• One-Loop QCD Spin Chain and its Spectrum
• Separation of variables for the Ruijsenaars system
• On The Baxter's Q - Operator for the XXX Spin Chain
• Analytic Bethe ansatz and functional equations for Lie superalgebra sl(r+1|s+1)
• A Generalized Q-operator for U_q(\hat(sl_2)) Vertex Models
• Gauss decomposition of trigonometric R-matrices
• Factorization of the transfer matrices for the quantum sl(2) spin chains and Baxter equation
• A Q-operator for the twisted XXX model
• Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
• Baxter Equation for Quantum Discrete Boussinesq Equation
• Baxter operators for the quantum sl(3) invariant spin chain

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