Locality in Quantum Systems
By M. B. Hastings. 2010
174 citations recorded by the source corpus.
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider 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 we use techniques that give very slightly weaker bounds for simplicity. This is a preliminary version of the lecture notes, with the goal of getting the notes out close to the end of the school. Comments welcome.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/63ce4eae667a551a025aa87148be18991f0b664d
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Localized shocks (2014, unknown): “This bound states that ‖[Wx(tw),Wy]‖ ≤ c0‖Wx‖ ‖Wy‖ ec1tw−c2|x−y|, (2.3) where c0, c1, c2 are constants that depend on the Hamiltonian.”
- Quasiparticle engineering and entanglement propagation in a quantum many-body system (2014, background): “The appearing constants are not unique [9, 10], but as a reasonable choice one may identify the Lieb–Robinson velocity with the maximal group velocity vmax g .”
- Chaos in quantum channels (2015, background): “Such behavior is reminiscent of the Lieb-Robinson bound on the commutator of local operators separated in time for systems with local interactions [29, 30, 31] and suggests identifying vB with the LiebRobinson velocity.”