The spectral gap of the ferromagnetic XXZ chain

Abstract

We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with Hamiltonian $H=-{\sum }_x{S}_x^{(1)}{S}_{x+1}^{(1)}+S_x^{(2)}{S}_{x+1}^{(2)}+\Delta S_x^{(3)}{S}_{x+1}^{(3)}$, is given by $\Delta -1$ for all $\Delta \ge 1$. 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 $S{U}_q(2)$ quantum group symmetry of the model.

arXiv comment20 pages, LaTeX, accepted for publication in Lett. Math. Phys

References in corpus (2)

• Ground states of the infinite q-deformed Heisenberg ferromagnet
• Quantum spin chains with quantum group symmetry

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