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 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.
Highlights
The seminal work of Polyakov on the O(n) models [1] opened an era in the study of quantum NonLinear Sigma Models (NLSM) in 1 + 1 dimensions
Using the ODE/IQFT correspondence we identify the algebra of extended conformal symmetry and describe the linear and Hermitian structures of the space of states occurring in the scaling limit of the Z2 invariant inhomogeneous six-vertex model
Instead of considering the full Hilbert space H occurring in the scaling limit of the spin chain, one could focus on its Z2 invariant sector and identify this with the space of states of the Euclidean black hole NLSM
Summary
The seminal work of Polyakov on the O(n) models [1] opened an era in the study of quantum NonLinear Sigma Models (NLSM) in 1 + 1 dimensions. The proposal of Ikhlef, Jacobsen and Saleur concerns a critical spin chain, belonging to the integrability class of a Z2 invariant inhomogeneous six-vertex model, which is a special case of the lattice system introduced by Baxter in 1971 [17] They present highly non-trivial arguments, including numerical evidence, that the infra-red behaviour of the spin chain is governed by the so-called Euclidean black hole NLSM [18,19,20,21,22,23,24,25,26,27]. Using the ODE/IQFT correspondence we identify the algebra of extended conformal symmetry and describe the linear and Hermitian structures of the space of states occurring in the scaling limit of the Z2 invariant inhomogeneous six-vertex model. A list of the central results of this work is given in the Summary section
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