August 4th-7th, 2014
Yukawa Institute for Theoretical Physics, Kyoto University
"Symmetry protected entanglement renormalization"
Sukhbinder Singh (Macquarie University, Sydney)
[Based on: SS and Guifre Vidal, Physical Review B, 88, 121108 (Rapid communications) (2013).]
Entanglement renormalization[1] is a real-space renormalization group (RG) transformation for quantum many-body systems.
It generates the multi-scale entanglement renormalization ansatz (MERA)[2],
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[3] to be a discrete realization of the holographic principle of string theory.
In this talk I will describe 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.
[1] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).
[2] G. Vidal, Phys. Rev. Lett. 101, 110501 (2008).
[3] B. Swingle, Phys. Rev. D 86, 065007 (2012).
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