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Abstract: These lecture notes focus on the application of ideas of locality, inparticular Lieb-Robinson bounds, to quantum many-body systems. We considerapplications including correlation decay, topological order, a higherdimensional Lieb-Schultz-Mattis theorem, and a nonrelativistic Goldstonetheorem. 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 intuitiveideas behind them, and in some cases we use techniques that give very slightlyweaker bounds for simplicity.This is a preliminary version of the lecture notes, with the goal of gettingthe notes out close to the end of the school. Comments welcome.

Author: M. B. Hastings

Source: https://arxiv.org/

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