## Abstract

In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ model at roots of unity, i.e., Δ = (q + q^{-1})/2 with q^{2N}= 1 for integer N ≥ 2. They found a certain pattern of degeneracies and linked it to the sl_{2}-loop symmetry present in the commensurable spin sector S^{z} = 0 mod N. We show that the degeneracies are due to an unusual type of zero-energy "transparent" excitation, the cyclic bound state. The cyclic bound states exist both in the commensurable and in the incommensurable sectors indicating a symmetry group present, of which sl_{2}-loop algebra is a partial manifestation. Our approach treats both sectors on even footing and allows us to obtain analytically an explicit expression for the degeneracies in the case N = 3.

Original language | English (US) |
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Pages (from-to) | 677-709 |

Number of pages | 33 |

Journal | Journal of Statistical Physics |

Volume | 105 |

Issue number | 3-4 |

DOIs | |

State | Published - Nov 2001 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Elementary excitations
- Integrable models
- Multiplets
- Quantum symmetry
- Spin chains