Causal structure of the entanglement renormalization ansatz

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.

References in corpus (5)

• A class of quantum many-body states that can be efficiently simulated
• Tensor network states and geometry
• Entanglement renormalization, scale invariance, and quantum criticality
• Unifying variational methods for simulating quantum many-body systems
• Simulation of time evolution with the MERA

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