Corner transfer matrix of generalised free Fermion vertex systems

Abstract

The Hamiltonian limit of the corner transfer matrix (CTM) of a generalised free Fermion vertex system of finite size leads to a quantum spin Hamiltonian of the particular form: \[ {\cal H}_N=-\sum_{n=1}^{N-1}\left\{ n\left( \sigma_n^x\sigma_{n+1}^x +\lambda\sigma_n^y\sigma_{n+1}^y +h(\sigma_n^z+\sigma_{n+1}^z) \right)\right\} \] Diagonalisation may be achieved for all pairs of parameters $(\lambda,h)$ with the use of some new elliptic polynomials which extend the class of special polynomials known so far in the context of CTM.