Lieb-Robinson bounds imply locality of interactions

Understand

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.