Geometric interpretation of the multi-scale entanglement renormalization ansatz

Understand

The multi-scale entanglement renormalization ansatz (MERA) is a tensor network representation for ground states of critical quantum spin chains, with a network that extends in an additional dimension corresponding to scale.

• Over the years several authors have conjectured, both in the context of holography and cosmology, that MERA realizes a discrete version of some geometry.
• However, while one proposal argued that the tensor network should be interpreted as representing the hyperbolic plane, another proposal instead equated MERA to de Sitter spacetime.
• In this \letter we show, using the framework of path integral geometry [A.