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

2001/06/28 by D. Braak, N. Andrei
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf

published as J.Stat.Phys. 105, pp.677-709 (2001) · 27 pages

arxiv created 2001/06/28 · arxiv updated 2009/11/30

Abstract

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.

Related

• The sl₂ loop algebra symmetry of the six-vertex model at roots of unity
• The complete one-loop spin chain for N=2 Super-Yang-Mills
• su(2) symmetry of XX spin chains
• The spectral gap of the ferromagnetic XXZ chain
• The spectral gap for the ferromagnetic spin-J XXZ chain