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Real-space renormalization yields finite correlations.

Publication ,  Journal Article
Barthel, T; Kliesch, M; Eisert, J
Published in: Physical review letters
July 2010

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law.

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Published In

Physical review letters

DOI

EISSN

1079-7114

ISSN

0031-9007

Publication Date

July 2010

Volume

105

Issue

1

Start / End Page

010502

Related Subject Headings

  • General Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Barthel, T., Kliesch, M., & Eisert, J. (2010). Real-space renormalization yields finite correlations. Physical Review Letters, 105(1), 010502. https://doi.org/10.1103/physrevlett.105.010502
Barthel, Thomas, Martin Kliesch, and Jens Eisert. “Real-space renormalization yields finite correlations.Physical Review Letters 105, no. 1 (July 2010): 010502. https://doi.org/10.1103/physrevlett.105.010502.
Barthel T, Kliesch M, Eisert J. Real-space renormalization yields finite correlations. Physical review letters. 2010 Jul;105(1):010502.
Barthel, Thomas, et al. “Real-space renormalization yields finite correlations.Physical Review Letters, vol. 105, no. 1, July 2010, p. 010502. Epmc, doi:10.1103/physrevlett.105.010502.
Barthel T, Kliesch M, Eisert J. Real-space renormalization yields finite correlations. Physical review letters. 2010 Jul;105(1):010502.

Published In

Physical review letters

DOI

EISSN

1079-7114

ISSN

0031-9007

Publication Date

July 2010

Volume

105

Issue

1

Start / End Page

010502

Related Subject Headings

  • General Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences