The $Z_2$ staggered vertex model and its applications

Abstract

New solvable vertex models can be easily obtained by staggering the spectral parameter in already known ones. This simple construction reveals some surprises: for appropriate values of the staggering, highly non-trivial continuum limits can be obtained. The simplest case of staggering with period two (the $Z_2$ case) for the six-vertex model was shown to be related, in one regime of the spectral parameter, to the critical antiferromagnetic Potts model on the square lattice, and has a non-compact continuum limit. Here, we study the other regime: in the very anisotropic limit, it can be viewed as a zig-zag spin chain with spin anisotropy, or as an anyonic chain with a generic (non-integer) number of species. From the Bethe-Ansatz solution, we obtain the central charge $c=2$, the conformal spectrum, and the continuum partition function, corresponding to one free boson and two Majorana fermions. Finally, we obtain a massive integrable deformation of the model on the lattice. Interestingly, its scattering theory is a massive version of the one for the flow between minimal models. The corresponding field theory is argued to be a complex version of the $C_2^{(2)}$ Toda theory.

38 pages, 14 figures, 3 appendices

References in corpus (2)

• Interacting anyons in topological quantum liquids: The golden chain
• Exact low temperature results for transport properties of the interacting resonant level model

Cited by in corpus (22)

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• 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
• An integrable modification of the critical Chalker-Coddington network model
• Integrable boundary conditions in the antiferromagnetic Potts model
• Lattice regularisation of a non-compact boundary conformal field theory
• The antiferromagnetic Potts model
• The continuum limit of $a_{N-1}^{(2)}$ spin chains
• Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
• Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
• Non compact continuum limit of two coupled Potts models
• On the scaling behaviour of an integrable spin chain with ${\mathcal{Z}}_r$ symmetry
• Integrability in anyonic quantum spin chains via a composite height model
• Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• Exact solution of a anisotropic $J_1-J_2$ spin chain with antiperiodic boundary condition
• Exact solution of an integrable anisotropic $J_1-J_2$ spin chain model
• Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-$\frac{1}{2}$ chain
• Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• Local height probabilities in a composite Andrews-Baxter-Forrester model