We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained Lieb-Robinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasi-locality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multi-dimensional Lieb-Schultz-Mattis Theorem.
CITATION STYLE
Nachtergaele, B., & Sims, R. (2009). Locality Estimates for Quantum Spin Systems. In New Trends in Mathematical Physics (pp. 591–614). Springer Netherlands. https://doi.org/10.1007/978-90-481-2810-5_39
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