Locality in quantum and Markov dynamics on lattices and networks.
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.
Hastings
M B
MB
T-13, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. hastings@cnls.lanl.gov