Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model

Abstract

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as the powerful analytic technique of the ODE/IQFT correspondence. The results indicate that the critical behaviour of the lattice system is described by the gauged $\mathrm{SL}(2)$ WZW model with certain boundary and reality conditions imposed on the fields. Our proposal revises and extends the conjectured relation between the lattice system and the Euclidean black hole non-linear sigma model that was made in the 2011 paper of Ikhlef, Jacobsen and Saleur.

152 pages, 26 figures, 5 tables, minor misprints corrected

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• Integrable boundary conditions for staggered vertex models
• An Ising-type formulation of the six-vertex model
• On solutions of the Bethe Ansatz for the Quantum KdV model
• Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
• On the scaling behaviour of an integrable spin chain with ${\mathcal{Z}}_r$ symmetry
• Spin chains with boundary inhomogeneities
• Feigin-Frenkel-Hernandez Opers and the QQ-system
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-$\frac{1}{2}$ chain
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models
• Universal Euler-Cartan Circuits for Quantum Field Theories
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum