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Entanglement Renormalization

G. Vidal
Phys. Rev. Lett. 99, 220405 – Published 28 November 2007

Abstract

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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  • Received 1 December 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.220405

©2007 American Physical Society

Authors & Affiliations

G. Vidal

  • School of Physical Sciences, the University of Queensland, QLD 4072, Australia
  • Institute for Quantum Information, California Institute for Technology, Pasadena, California 91125, USA

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Issue

Vol. 99, Iss. 22 — 30 November 2007

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