  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.
