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

  • Martin Kliesch
  • Christian Gogolin
  • Jens Eisert
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.

Keywords

Interaction Graph Local Observable Fermionic Operator Heisenberg Picture Tensor Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We thank Earl T. Campbell, Mathis Friesdorf and Albert H. Werner for comments. We acknowledge support from the EU (Q-Essence, Raquel), the BMBF (QuOReP), the ERC (Taq), and the Studienstiftung des Deutschen Volkes.

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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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