Quasilocality Estimates in Quantum Lattice Systems

In the 1970s, Lieb and Robinson introduced an essential upper bound on the speed of propagation of information for specific classes of models in quantum statistical mechanics. Since then, the Lieb-Robinson bounds have been extended to encompass a broad class of quantum lattice system models and serve as a basis for the rigorous proof of the existence of Heisenberg dynamics in the thermodynamic limit. Quasilocal maps, which obey Lieb-Robinson type bounds, continue to appear in research questions. This talk will introduce a general framework for the analysis of quantum lattice systems and a broad overview of the Hastings method for analysis of perturbed systems. When combined with the results from understanding quasilocal maps, observations made on these topics in finite systems can be extended to the thermodynamic limit.