Lieb-Robinson bounds imply locality of interactions

• URL: http://arxiv.org/abs/2006.10062v2
• Date: Mon, 28 Sep 2020 14:21:02 GMT
• Title: Lieb-Robinson bounds imply locality of interactions
• Authors: Henrik Wilming and Albert H. Werner
• Abstract summary: We show that Lieb-Robinson bounds are equivalent to the locality of the interactions. A system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the interactions decay exponentially in space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviours as well as fermionic lattice models. As a side-result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.

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