Some properties for the low-lying spectrum of the ferromagnetic, quantum XXZ spin system
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.
Keywords
Cite
@article{arxiv.math-ph/0106024,
title = {Some properties for the low-lying spectrum of the ferromagnetic, quantum XXZ spin system},
author = {Shannon Starr},
journal= {arXiv preprint arXiv:math-ph/0106024},
year = {2007}
}
Comments
221 pages, 22 figures, contains one Matlab script and one Mathematica script "in the source"