Some properties for the low-lying spectrum of the ferromagnetic, quantum XXZ spin system
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Some properties for the low-lying spectrum of the ferromagnetic, quantum XXZ spin system

  • Author(s): Starr, Shannon
  • et al.

Published Web Location

https://arxiv.org/pdf/math-ph/0106024.pdf
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Abstract

In this thesis we present three results about the ferromagnetic quantum XXZ model: 1) Existence of a spectral gap above all infinite-volume ground states in one dimension for any choice of spin S>1/2 (for S=1/2 this was already known); 2) Characterization of one-dimensional "droplet" states as ground states of the spin-1/2 model with up spin boundary fields; 3) An upper bound for the spectral gap above the spin-1/2 interface ground states in dimension two and higher. The upper bound vanishes as 1/R^2, where R is the linear size of the system. This thesis contains research performed in collboration with other authors: O. Bolina, P. Contucci, T. Koma, B. Nachtergaele.

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