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

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

2001-06-23

arxiv.org/abs/math-ph/0106024v1

Physics

Mathematical Physics

221 pages, 22 figures, contains one Matlab script and one Mathematica script "in the source"

Scientific paper

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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