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Entanglement Renormalization

Vidal, G. (2007) Entanglement Renormalization. Physical Review Letters, 99 (22). Art. No. 220405. ISSN 0031-9007. doi:10.1103/PhysRevLett.99.220405.

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We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.

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Additional Information:©2007 The American Physical Society. (Received 1 December 2006; published 28 November 2007) The author appreciates conversations with I. Cirac, J.I. Latorre, T. Osborne, D. Poulin, J. Preskill, and, very specially, with F. Verstraete, whose advise was crucial to find a fast disentangling algorithm. USA NSF Grant No. EIA-0086038 and an Australian Research Council Grant No. FF0668731 are acknowledged.
Issue or Number:22
Record Number:CaltechAUTHORS:VIDprl07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9242
Deposited By: Archive Administrator
Deposited On:29 Nov 2007
Last Modified:08 Nov 2021 20:57

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