Rapid mixing implies exponential decay of correlations

@article{Kastoryano2013RapidMI,
  title={Rapid mixing implies exponential decay of correlations},
  author={Michael J. Kastoryano and Jens Eisert},
  journal={Journal of Mathematical Physics},
  year={2013},
  volume={54},
  pages={102201-102201}
}
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 prove, furthermore, that if the Log-Sobolev constant is independent of the system size, then the… 

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