Multi-scale entanglement renormalization ansatz Tensor network

[kodama]

as a new proposal for QGhttp://arxiv.org/abs/1502.05385
Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
Glen Evenbly, Guifre Vidal
(Submitted on 18 Feb 2015)
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and G. Vidal, arXiv:1412.0732] to the Euclidean time evolution operator e−βH for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows TNR with a renormalization group flow in the space of wave-functions and Hamiltonians (and not just in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

 

[atyy]

It is not a new proposal. It is mainly about the AdS/CFT conjecture of string theory. If the conjecture is right, are there relatively simple ways we can understand how it works? The AdS/MERA picture was proposed by Brian Swingle (Physics Monkey) to help understand AdS/CFT using tools from condensed matter physics. Among the key papers preceding AdS/MERA are Juan Maldacena's thermofield double paper, the Ryu-Takayanagi proposal linking entanglement entropy and area, and Guifre Vidal's MERA. Also, there are many papers linking renormalization and holography, and the MERA is a form of renormalization. What the MERA seems to offer is a simple picture of how the various ideas (entanglement, geometry, renormalization) can be linked together.