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

TL;DR

This paper reviews Lieb-Robinson bounds in quantum many-body systems, highlighting their implications for the speed of correlation propagation and the simulation of system dynamics and states.

Contribution

It introduces a Lieb-Robinson bound for local Liouvillians in open and closed systems, extending the concept to time-dependent scenarios.

Findings

Lieb-Robinson bounds establish a maximum speed for correlation spread.

The bounds have important implications for simulating quantum dynamics.

They influence understanding of ground and stationary state properties.

Abstract

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