TY - JOUR

T1 - Symmetry-protected entanglement renormalization

AU - Singh, Sukhwinder

AU - Vidal, Guifre

PY - 2013/9/24

Y1 - 2013/9/24

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84884841571&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.88.121108

DO - 10.1103/PhysRevB.88.121108

M3 - Article

AN - SCOPUS:84884841571

SN - 1098-0121

VL - 88

SP - 121108-1-121108-5

JO - Physical Review B: Condensed Matter and Materials Physics

JF - Physical Review B: Condensed Matter and Materials Physics

IS - 12

M1 - 121108

ER -