Corner transfer matrix of generalised free Fermion vertex systems

1993/08/06 by H. -P. Eckle, Hans-Peter Eckle, Eckle, H. -P. +2
Computer Science · Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Matrix Theory and Algorithms #Random Matrices and Applications #Spectral Theory in Mathematical Physics #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/9308009

(No changes of text, replaced LaTeX file fits better to US legal letter) 29 pages, LaTeX, HPETTT-CTM-93-02

openalex publication_date 1993/08/06 · arxiv created 1993/08/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=-∑_n=1^N-1\ n( σ_n^xσ_n+1^x +λσ_n^yσ_n+1^y +h(σ_n^z+σ_n+1^z) )\ 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.

Related

• Spectrum of an Elliptic Free Fermionic Corner Transfer Matrix Hamiltonian
• Infinite dimensional symmetry of corner transfer matrices
• Edge Hamiltonian for Free Fermion Quantum Hall Models
• Factorial Fock free fermions
• Integrable Vertex Models with General Twists