Excitation Spectra of Spin Models constructed from Quantized Affine Algebras of type $B_n^{(1)}$, $D_n^{(1)}$

TL;DR

This paper computes the excitation spectra of spin models derived from quantized affine algebras of types B and D, confirming their mass spectra and providing explicit fusion constructions.

Contribution

It introduces the explicit fusion construction for quantized affine algebras of types B and D and computes their excitation spectra in the anti-ferromagnetic regime.

Findings

Spectra agree with factorized S-matrix results

Explicit fusion construction for B and D types

Spectral computations confirm theoretical predictions

Abstract

The energy and momentum spectrum of the spin models constructed from the vector representation of the quantized affine algebras of type $\B$ and $\D$ are computed using the approach of Davies et al. \cite{DFJMN92}. The results are for the anti-ferromagnetic (massive) regime, and they agree with the mass spectrum found from the factorized S--matrix theory by Ogievetsky et al. \cite{ORW87}. The other new result is the explicit realization of the fusion construction for the quantized affine algebras of type $\B$ and $\D$.}