Chapter

Locality in quantum systems

Matthew B Hastings

in Quantum Theory from Small to Large Scales

Published in print May 2012 | ISBN: 9780199652495
Published online September 2012 | e-ISBN: 9780191741203 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199652495.003.0003

Series: Lecture Notes of the Les Houches Summer School

Locality in quantum systems

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This chapter focuses on the application of ideas of locality, in particular Lieb–Robinson bounds, to quantum many-body systems. It considers applications including correlation decay, topological order, a higher dimensional Lieb–Schultz–Mattis theorem, and a nonrelativistic Goldstone theorem. The emphasis is on trying to show the ideas behind the calculations. As a result, the proofs are only sketched with an emphasis on the intuitive ideas behind them, and in some cases techniques that give very slightly weaker bounds are used for simplicity.

Keywords: locality; Lieb–Robinson bounds; quantum many-body; topological order

Chapter.  21030 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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