致谢#

These lecture notes build largely on material to be published as a book, Quantum Spin Systems—A Computational Perspective, by Cambridge University Press. The opportunity to lecture at the XIV Training Course in the Physics of Strongly Correlated Systems (Vietri sul Mare, Salerno, Italy, in October 2009) prompted me to prepare a condensed version of this as of yet unfinished work (which will discuss a larger set of models and computational methods). These lecture notes cover the topics I discussed at Vietri sul Mare, but I have added more background and details. Some of the applications have been complemented with recent results. As in my lectures, the target audience for these notes is graduate students and postdocs who are entering the field of quantum magnetism, or some related area in where quantum spin models are of interest, and need a source for elementary concepts and calculations. I believe that this material could also form the core of a one-semester advanced topics course in quantum magnetism (focused on concepts and numerical calculations).

I would like to thank the organizers of the Salerno Training Course, Professors Ferdinando Mancini and Adolfo Avella, for the invitation to lecture and publish these notes. I also thank the students at Vietri sul Mare for their enthusiasm. I am grateful to Ying Tang for her careful reading of the manuscript. I thank Cambridge University Press and the American Institute of Physics for agreeing on the copyright issues related to dual publication of most of the material presented here. Excerpts are printed with the permission of Cambridge University Press. Some of this work was supported by the NSF under Grant No. DMR-0803510.