Wednesday, March 27, 2013

1303.6304 (Michael J. Kastoryano et al.)

Rapid mixing implies exponential decay of correlations    [PDF]

Michael J. Kastoryano, Jens Eisert
We provide an analysis of the correlation properties of spin and fermionic systems on a lattice evolving according to open system dynamics generated by a local primitive Liouvillian. We show that if the Liouvillian has a spectral gap which is independent of the system size, then the correlations between local observables decay exponentially as a function of the distance between their supports. We show, furthermore, that if the Log-Sobolev constant is independent of the system size, then the system satisfies clustering of correlations in the mutual information - a much more stringent form of correlation decay. As a corollary, we obtain a stability theorem for local distant perturbations. We also show that gapped for free-fermionic systems, exhibit clustering of correlations in the covariance and in the mutual information. We conclude with a discussion of the implications of these results for the classical simulation of open quantum systems with matrix-product operators and the robust dissipative preparation of topologically ordered states of lattice spin systems.
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