Causal structure of the entanglement renormalization ansatz

TL;DR

This paper reveals that MERA can be understood through a causality structure akin to de Sitter space, linking tensor networks, quantum dynamics, and spacetime geometry, and suggesting extensions to quantum field theory.

Contribution

It reformulates MERA as a causality-constrained quantum dynamics with a de Sitter space structure, clarifying its geometric interpretation and potential generalizations.

Findings

MERA corresponds to a causality structure of de Sitter space.

The volume of spacetime regions relates to variational parameters.

Supports the connection between MERA and hyperbolic geometry in AdS-CFT.

Abstract

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat spacelike boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.