The spectral gap of the ferromagnetic XXZ chain

1995/12/15 by Tohru Koma, Bruno Nachtergaele · 1 citation
Physics and Astronomy · #cond-mat

paper · pdf

published as Lett. Math. Phys., 40 (1997) 1-16 · 20 pages, LaTeX, accepted for publication in Lett. Math. Phys

arxiv created 1995/12/15 · arxiv updated 2009/11/30

Abstract

We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with Hamiltonian H=-∑_x S⁽¹⁾_xS⁽¹⁾_x+1+S⁽²⁾_xS⁽²⁾_x+1 +ΔS⁽³⁾_xS⁽³⁾_x+1, is given by Δ-1 for all Δ≥ 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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• Spectral statistics and energy-gap scaling in k-local spin Hamiltonians

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