Phys. Rev. Lett. 93, 140402 (2004) [4 pages]Locality in Quantum and Markov Dynamics on Lattices and NetworksReceived 28 May 2004; published 28 September 2004 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. © 2004 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.93.140402
DOI:
10.1103/PhysRevLett.93.140402
PACS:
05.30.–d, 03.67.Lx
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