Entanglement renormalization.

By Guifré Vidal. 2005

913 citations recorded by the source corpus.

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.

How researchers see this paper

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1. D. Harlow
2. A. Nahum
3. R. Myers
4. B. Yoshida
5. Paweł Caputa
6. Thomas Hartman
7. T. Takayanagi
8. Pasquale Calabrese

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Well-known examples include the so called projected entangled-pair states (PEPS) [260, 261] and the multiscale entanglement renormalization ansatz (MERA) [264].”
• Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, methodology): “Our second class of adaptive circuits realizes a multiscale entanglement renormalization ansatz (MERA) [19, 20] using (spatially) local unitary gates and local Bell-pair measurements.”
• Supervised Learning with Tensor Networks (2016, methodology): “While applications of MPS to machine learning have been a success, one aim of the present work is to have tensor networks play a more central role in developing learning models; another is to more easily incorporate powerful algorithms and tensor networks which generalize MPS developed by the physic”
• Lattice gauge theory simulations in the quantum information era (2016, background): “related to the real space RGprocedure, such as tree tensor networks (TTN) [74–76] and multi-scale entanglement renormalisation ansatz [77].”
• Entanglement entropy from a holographic viewpoint (2012, background): “One way to make this idea concrete seems to employ the conjectured connection [187] between the AdS/CFT and the multi scale entanglement renormalization (MERA) [188] (see also [189]).”