Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz

Abstract

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for the Bethe eigenvalues of the Q-operator is derived. A proof is given for states which contain up to three Bethe roots. Further evidence is provided by relating the findings to the six-vertex fusion hierarchy. For the XXZ spin-chain we analyze the cases when the deformation parameter of the underlying quantum group is evaluated both at and away from a root of unity.

32 pages

References in corpus (9)

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• Finite lattice Bethe ansatz systems and the Heun equation
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• Loop symmetry of integrable vertex models at roots of unity
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Cited by in corpus (12)

• The ODE/IM Correspondence
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• A Q-operator for the twisted XXX model
• Baxter Q-operators of the XXZ chain and R-matrix factorization
• Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
• Noncompact sl(N) spin chains: BGG-resolution, Q-operators and alternating sum representation for finite dimensional transfer matrices
• Auxiliary matrices on both sides of the equator
• Root of unity symmetries in the 8 and 6 vertex models
• A Q-operator for the quantum transfer matrix
• Evaluation of the operatorial Q-system for non-compact super spin chains
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin