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  Correlations in Quantum Spin Systems from the Boundary Effect

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Referee this paper: arXiv:1308.6030 by Jaeyoon Cho

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

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Abstract: We introduce the boundary effect on the ground state as an attribute of general local spin systems that restricts the correlations in the ground state. To this end, we introduce what we call a boundary effect function, which characterises not only the boundary effect, but also the thermodynamic limit of the ground state. We prove various aspects of the boundary effect function to unfold its relationship to other attributes of the system such as a finite spectral gap above the ground state, two-point correlation functions, and entanglement entropies. In particular, it is proven that an exponentially decaying boundary effect function implies the exponential clustering of two-point correlation functions in arbitrary spatial dimension, the entanglement area law in one dimension, and the logarithmically corrected area law in higher dimension. It is also proven that gapped local spin systems with nondegenerate ground states ordinarily fall into that class. In one dimension, the area law can also result from a moderately decaying boundary effect function, in which case the system is thermodynamically gapless.

requested Feb 17, 2017 by David B Roberts (135 points)
summarized by Arnold Neumaier
paper authored Aug 27, 2013 to quant-ph by  (no author on PO assigned yet) 
  • [ revision history ]
    edited Feb 18, 2017 by Arnold Neumaier

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