 95533 Tohru Koma, Bruno Nachtergaele
 The spectral gap of the ferromagnetic XXZ chain
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Dec 15, 95

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Abstract. We prove that the spectral gap of the spin1/2 ferromagnetic XXZ chain
with Hamiltonian $H=\sum_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1}
+\Delta S^{(3)}_xS^{(3)}_{x+1}$, is given by $\Delta1$ for all
$\Delta\geq 1$. This is the gap in the spectrum of the infinite chain
in any of its ground states, the translation invariant ones as well as
the kink ground states, which contain an interface between an {\it
up\/} and a {\it 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 $SU_q(2)$ quantum group
symmetry of the model.
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