Locality in Quantum and Markov Dynamics on Lattices and Networks

Details Locality in Quantum and Markov Dynamics on Lattices and Networks Locality in Quantum and Markov Dynamics on Lattices and Networks

2004-05-25

arxiv.org/abs/cond-mat/0405587v1

Phys. Rev. Lett. 93, 140402 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 0 figures

Scientific paper

10.1103/PhysRevLett.93.140402

We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we prove that ground or stationary state correlation functions can be written as a piece decaying exponentially in space plus a term set by matrix elements between the low-lying states. The key to the proof is a local approximation to the negative energy, or annihilation, part of an operator in a gapped system. Applications to numerical simulation of quantum systems and to networks are discussed.

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