ON-LINE QLunch: Finite group velocity implies quasi-locality of interactions

Speaker: Henrik Wilming, ETH Zürich

Title: Finite group velocity implies quasi-locality of interactions

Abstract:

Spin systems with exponentially decaying k-body interactions have a finite group velocity for the propagation of correlations.

Lieb-Robinson bounds formalize this notion and form the basis for a variety of important results in many-body physics. We show that an assumed (or measured) bound on propagation of correlations in form of Lieb-Robinson bounds conversely also implies the locality of the underlying Hamiltonian: A spin system fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space.