A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models

TL;DR

This paper explores a family of spin-S chain Hamiltonians, revealing their low-energy behavior aligns with SU(2)_k Wess-Zumino-Witten models, and provides insights into their spectra and ground states.

Contribution

It introduces a unified framework connecting spin-S chains with SU(2)_k WZW models, extending known models and analyzing their spectra and ground states.

Findings

For S=1/2, recovers the Haldane-Shastry model.

For general S, low-energy theory matches SU(2)_k WZW with k=2S.

Ground state of S=1 model is a Pfaffian for even N.

Abstract

We investigate a family of spin-S chain Hamiltonians recently introduced by one of us. For S=1/2, it corresponds to the Haldane-Shastry model. For general spin S, we find indication that the low-energy theory of these spin chains is described by the SU(2)_k Wess-Zumino-Witten model with coupling k=2S. In particular, we investigate the S=1 model whose ground state is given by a Pfaffian for even number of sites N. We reconcile aspects of the spectrum of the Hamiltonian for arbitrary N with trial states obtained by Schwinger projection of two Haldane-Shastry chains.