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: \[ {\cal H}_N=-\sum_{n=1}^{N-1}\left\{ n\left( σ_n^xσ_{n+1}^x +λσ_n^yσ_{n+1}^y +h(σ_n^z+σ_{n+1}^z) \right)\right\} \] Diagonalisation may be achieved for all pairs of parameters $(λ,h)$ with the use of some new elliptic polynomials which extend the class of special polynomials known so far in the context of CTM.