Corner transfer matrix of generalised free Fermion vertex systems

TL;DR

This paper derives a quantum spin Hamiltonian from the corner transfer matrix of a generalized free Fermion vertex system and introduces new elliptic polynomials for its diagonalization across all parameter pairs.

Contribution

It presents a novel connection between corner transfer matrices and a specific quantum spin Hamiltonian, introducing new elliptic polynomials for diagonalization.

Findings

Diagonalization possible for all parameter pairs using new elliptic polynomials

Extension of special polynomial classes in the context of CTM

Explicit form of the Hamiltonian derived from CTM limit

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.