Real-space renormalization yields finite correlations


Journal Article

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. © 2010 The American Physical Society.

Full Text

Duke Authors

Cited Authors

  • Barthel, T; Kliesch, M; Eisert, J

Published Date

  • July 2, 2010

Published In

Volume / Issue

  • 105 / 1

Electronic International Standard Serial Number (EISSN)

  • 1079-7114

International Standard Serial Number (ISSN)

  • 0031-9007

Digital Object Identifier (DOI)

  • 10.1103/PhysRevLett.105.010502

Citation Source

  • Scopus