Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model

Abstract

The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses $\mathrm{U}(1)$ invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ as well as translational invariance. The special properties of the lattice system that possesses an additional ${\mathcal{Z}}_r$ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.

29 pages, 2 figures; minor typos fixed, references added, published version

References in corpus (10)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Hirota equation as an example of integrable symplectic map
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• The antiferromagnetic transition for the square-lattice Potts model
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling
• The $Z_2$ staggered vertex model and its applications
• Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain
• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model

Cited by in corpus (8)

• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Lattice regularisation of a non-compact boundary conformal field theory
• Integrable boundary conditions for staggered vertex models
• An Ising-type formulation of the six-vertex model
• On the scaling behaviour of an integrable spin chain with ${\mathcal{Z}}_r$ symmetry
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models