Locality Estimates for Quantum Spin Systems

Details Locality Estimates for Quantum Spin Systems Locality Estimates for Quantum Spin Systems

2007-12-20

arxiv.org/abs/0712.3318v1

in: Sidoravicius, Vladas (Ed.), New Trends in Mathematical Physics. Selected contributions of the XVth International Congress

Physics

Mathematical Physics

Contribution for the proceedings of ICMP XV, Rio de Janeiro, 2006

Scientific paper

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.

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