Quantum Spin Systems

2004/09/02 by Bruno Nachtergaele, Nachtergaele, Bruno · 2 citations
Mathematics · Physics and Astronomy · #82B10 #82B20 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:82B10 #msc:82B20

paper · pdf · doi:10.48550/arxiv.math-ph/0409006

Article for the Encyclopedia of Mathematical Physics (Elsevier)

arxiv created 2004/09/02 · arxiv updated 2009/12/01

Abstract

This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is described. Then, three short sections are devoted to Spontaneaous Symmetry Breaking, Phase transitions, and Dynamcis.

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• The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds
• Quantum correlations versus spin magnitude: Transition to the classical limit

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