Spectrum of an Elliptic Free Fermionic Corner Transfer Matrix Hamiltonian

TL;DR

This paper computes the eigenvalues of the Corner Transfer Matrix Hamiltonian for the elliptic eight vertex free fermion model in the anisotropic case, revealing equally spaced energy levels and validating results numerically.

Contribution

It provides the first explicit calculation of the spectrum for this specific elliptic model using generating functions, enhancing understanding of its spectral properties.

Findings

Eigenvalues are explicitly computed for the anisotropic case.

Spectrum consists of equally spaced energy levels.

Results are verified through numerical checks.

Abstract

The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic $R$ matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels.