Letters in Mathematical Physics

, Volume 40, Issue 1, pp 1–16

The Spectral Gap of the Ferromagnetic XXZ-Chain


DOI: 10.1023/A:1007351803403

Cite this article as:
KOMA, T. & NACHTERGAELE, B. Letters in Mathematical Physics (1997) 40: 1. doi:10.1023/A:1007351803403


We prove that the spectral gap of the spin-\(\frac{1}{2}\) ferromagnetic XXZ-chain with HamiltonianH=−Σ_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1}+\Delta S^{(3)}_xS^{(3)}_{x+1}, is given by Δ-1 for all Δ≥1. This is the gap in the spectrum of the infinite chainin any of its ground states, the translation invariant ones as well asthe kink ground states, which contain an interface between an up and a down region.In particular, this shows that the lowest magnon energy is not affected by the presence of a domain wall. This surprising fact is a consequence of the SUq(2)quantum group symmetry of the model.

quantum spin chainsHeisenberg modelferrp,agmetoc XXZ-chainkink ground statesspectral gapquantum group symmetry.

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

    • 1
    • 2
  1. 1.Department of PhysicsGakushuin University, Mejiro, Toshima-ku, TokyoJapan
  2. 2.Department of PhysicsPrinceton UniversityPrincetonU.S.A.