The $Z_2$ staggered vertex model and its applications

TL;DR

This paper explores a $Z_2$ staggered vertex model, revealing its continuum limits, connections to spin chains and anyonic systems, and deriving its conformal field theory and integrable deformations.

Contribution

It introduces a new $Z_2$ staggered vertex model, analyzes its continuum limit, and links it to complex Toda theories and massive integrable deformations.

Findings

Central charge c=2 from Bethe-Ansatz

Continuum spectrum includes one free boson and two Majorana fermions

Massive deformation related to flow between minimal models

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.