On the Spectrum of the XXZ-chain at roots of unity

Details On the Spectrum of the XXZ-chain at roots of unity On the Spectrum of the XXZ-chain at roots of unity

2001-06-28

arxiv.org/abs/cond-mat/0106593v1

J.Stat.Phys. 105, pp.677-709 (2001)

Physics

Condensed Matter

Statistical Mechanics

27 pages

Scientific paper

In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ-model at Delta = (q+q^{-1})/2 and q^{2N}=1 for integer N >1. They found a certain pattern of degeneracies and linked it to the sl(2)-loop symmetry present in the commensurable spin sector (N divides S^z). We show that the degeneracies are due to zero-energy, transparent excitations, the cyclic bound states. These exist both in commensurable and incommensurable sectors, indicating a symmetry, of which sl(2)-loop is a partial manifestation. Our approach treats both sectors on even footing and yields an analytical expression for the degeneracies in the case N = 3.

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