Lieb-Robinson Bounds and the Simulation of Time-Evolution of Local Observables in Lattice Systems

Chapter
Part of the Mathematical Physics Studies book series (MPST)

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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Martin Kliesch
    • 1
  • Christian Gogolin
    • 1
  • Jens Eisert
    • 1
  1. 1.Dahlem Center for Complex Quantum SystemsFreie Universität BerlinBerlinGermany

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