Single Particle Excitations in the Lattice E_8 Ising Model

TL;DR

This paper derives analytic expressions for the energies of single particle excitations in the lattice E_8 Ising model, revealing extended Brillouin zones and comparing results with exact diagonalizations and fermionic representations.

Contribution

It provides the first analytic formulas for the excitation energies of all eight quasi-particles in the lattice E_8 Ising model, linking them to Brillouin zone extensions.

Findings

All excitations have extended Brillouin zones up to 12π.

Analytic expressions match well with exact diagonalization results.

Results connect excitation spectra with E_8 fermionic characters.

Abstract

We present analytic expressions for the single particle excitation energies of the 8 quasi-particles in the lattice $E_8$ Ising model and demonstrate that all excitations have an extended Brillouin zone which, depending on the excitation, ranges from 0<P < 4\pi to 0< P< 12 \pi. These are compared with exact diagonalizations for systems through size 10 and with the E_8 fermionic representations of the characters of the critical system in order to study the counting statistics.