A Q-operator for the twisted XXX model

Abstract

Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are needed to ensure convergence of the Q-operator construction and derive a quantum Wronskian relation which implies two different sets of Bethe ansatz equations, one above the other below the "equator" of total spin zero. We discuss the limit to periodic boundary conditions at the end and explain how this construction might be useful in the context of correlation functions on the infinite lattice. We also identify a special subclass of solutions to the quantum Wronskian for chains up to a length of 10 sites and possibly higher.

19 pages

References in corpus (4)

• Traces on the Sklyanin algebra and correlation functions of the eight-vertex model
• Reduced qKZ equation and correlation functions of the XXZ model
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• Auxiliary matrices on both sides of the equator

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• Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
• On quantum separation of variables beyond fundamental representations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• Evaluation of the operatorial Q-system for non-compact super spin chains
• A Q-operator for the quantum transfer matrix
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Transfer matrices of rational spin chains via novel BGG-type resolutions