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This is an introductory text reviewing Lieb-Robinson bounds for open andclosed quantum many-body systems. We introduce the Heisenberg picture fortime-dependent local Liouvillians and state a Lieb-Robinson bound that givesrise to a maximum speed of propagation of correlations in many body systems oflocally interacting spins and fermions. Finally, we discuss a number ofimportant consequences concerning the simulation of time evolution andproperties of ground states and stationary states.

Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems