HEP Theory Journal Club

The idea of Entanglement Renormalization:
the MERA tensor network and relation to AdS/CFT

Ioannis Tsiares

McGill

The Hilbert space of a usual quantum many-body system is exponentially large. The question of whether or not there is a class of quantum many-body states that can be more efficiently described arises naturally (both for theoretical and numerical reasons). Representing a state with a network of tensors turns out to be the key ingredient to the answer. I will try to describe the basics of tensor networks and mainly I will focus on a particular tensor network, called MERA (Multi-scale Entanglement Renormalization Ansatz). Among other things, this tensor network turns out to give us a new perspective on the idea of renormalization. It roughly suggests that in addition to the usual coarse-graining procedure, we also have to consider how entanglement is coarse-grained (entanglement renormalization). Finally, I will try to illustrate how MERA is related to a discrete version of AdS space and why it is a toy model of AdS/CFT.