Symmetry-protected entanglement renormalization

Sukhwinder Singh*, Guifre Vidal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multiscale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently describing a large class of many-body ground states, including those of systems at a quantum critical point or with topological order. The MERA has also been proposed to be a discrete realization of the holographic principle of string theory. Here we propose the use of symmetric tensors as a mechanism to build a symmetry-protected RG flow, and discuss two important applications of this construction. First, we argue that symmetry-protected entanglement renormalization produces the proper structure of RG fixed points, namely, a fixed-point for each symmetry-protected phase. Second, in the context of holography, we show that by using symmetric tensors, a global symmetry at the boundary becomes a local symmetry in the bulk, thus explicitly realizing in the MERA a characteristic feature of the AdS/CFT correspondence.

Original languageEnglish
Article number121108
Pages (from-to)121108-1-121108-5
Number of pages5
JournalPhysical Review B: Condensed Matter and Materials Physics
Issue number12
Publication statusPublished - 24 Sept 2013


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