An Area Law for One Dimensional Quantum Systems

@article{Hastings2007AnAL,
  title={An Area Law for One Dimensional Quantum Systems},
  author={M. Hastings},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2007},
  volume={2007},
  pages={08024}
}
  • M. Hastings
  • Published 2007
  • Mathematics, Physics
  • Journal of Statistical Mechanics: Theory and Experiment
  • We prove an area law for the entanglement entropy in gapped one-dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on matrix product states which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, the bound on Von Neumann entropy implies a bound on Renyi entropy for sufficiently large α<1 and implies… CONTINUE READING

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