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

Daniel Braak, Natan Andrei

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 q2N= 1 for integer N ≥ 2. They found a certain pattern of degeneracies and linked it to the sl2-loop symmetry present in the commensurable spin sector Sz = 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 sl2-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 languageEnglish (US)
Pages (from-to)677-709
Number of pages33
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Nov 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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


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