Real-space renormalization yields finite correlations

Details Real-space renormalization yields finite correlations Real-space renormalization yields finite correlations

2010-03-11

arxiv.org/abs/1003.2319v2

Phys. Rev. Lett. 105, 010502 (2010)

Physics

Quantum Physics

7 pages, 6 figures; final version, featuring an addendum to the published article

Scientific paper

10.1103/PhysRevLett.105.010502

Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually finitely correlated states, 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 shown further that there exist other efficiently contractible schemes violating the area law.

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