Final PhD Seminar

Scaling limit of the Z2 invariant spin chain

Mr Sergii Koval
Theoretical Physics, ANU

The inhomogeneous six-vertex model is a 2D multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour, which have remained mostly unexplored. For general values of the parameters and twisted boundary conditions, the model possesses U(1) invariance. We discuss the restrictions imposed on the parameters for which additional global symmetries that are consistent with the integrable structure arise. The aforementioned general study laid the foundation for performing a detailed study of the scaling limit of a certain critical, integrable Z2 invariant spin chain subject to twisted boundary conditions. It is mainly based on a numerical analysis of the Bethe ansatz equations accompanied by the powerful analytic technique of the ODE/IQFT correspondence. The outcome of our study indicates 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. Originally, the results that are presented in this thesis have been published in the papers arXiv:2010.10613, 2010.10615, 1903.05033, which revise and extend 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.

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