Symmetry protected entanglement renormalization

TL;DR

This paper introduces symmetry protected entanglement renormalization using symmetric tensors within MERA, enabling the proper classification of phases and a realization of holographic duality with boundary symmetries becoming bulk gauge symmetries.

Contribution

It proposes a novel use of symmetric tensors in MERA to create symmetry protected RG flows and demonstrates their role in fixed-point structure and holographic duality.

Findings

Symmetry protected RG fixed points correspond to each phase.

Global boundary symmetries become local bulk symmetries in MERA.

The approach explicitly realizes features of AdS/CFT correspondence.

Abstract

Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multi-scale 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. In this paper 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.