Q-operators in the six-vertex model

Abstract

In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra $U_q(\widehat{sl(2)})$. Taking a special limit in this $R$-matrix we obtained new formulas for the $Q$-operators acting in the tensor product of representation spaces with arbitrary complex spin. Here we use a different strategy and construct $Q$-operators as integral operators with factorized kernels based on the original Baxter's method used in the solution of the eight-vertex model. We compare this approach with the method developed in [1] and find the explicit connection between two constructions. We also discuss a reduction to the case of finite-dimensional representations with (half-) integer spins.

18 pages, no figures

References in corpus (24)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• High energy QCD as a completely integrable model
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• A Shortcut to the Q-Operator
• Hidden Grassmann structure in the XXZ model
• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
• Q-operator and T-Q relation from the fusion hierarchy
• Bethe Ansatz for QCD Pomeron,
• Baxter's Q-operator for the homogeneous XXX spin chain
• On the Yang-Baxter equation for the six-vertex model
• Exercises with the universal R-matrix
• On The Baxter's Q - Operator for the XXX Spin Chain
• Quantum geometry of 3-dimensional lattices
• Yang-Baxter equation, parameter permutations, and the elliptic beta integral
• Universal integrability objects
• Baxter operators with deformed symmetry
• Commuting difference operators with elliptic coefficients from Baxter's vacuum vestors
• An integrable 3D lattice model with positive Boltzmann weights
• Baxter Q-operators of the XXZ chain and R-matrix factorization
• Baxter operators for arbitrary spin II
• Baxter operators for arbitrary spin
• The Large N Limits of the Chiral Potts Model
• The integrable structure of nonrational conformal field theory

Cited by in corpus (17)

• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• Yang-Baxter Maps, Discrete Integrable Equations and Quantum Groups
• Construction of $R$-matrices for symmetric tensor representations related to $U_q(\widehat{s{l}_n})$
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• 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
• A new generalisation of Macdonald polynomials
• From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
• An Ising-type formulation of the six-vertex model
• The Yang-Baxter relation and gauge invariance
• The non-compact XXZ spin chain as stochastic particle process
• Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables
• Q-operators for higher spin eight vertex models with an even number of sites
• Q-operators for higher spin eight vertex models with a rational anisotropy parameter
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin