The $Z_2$ staggered vertex model and its applications

Understand

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.