Causal structure of the entanglement renormalization ansatz. (English) Zbl 1451.81062
Summary: 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 space-like 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.
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81P42 | Entanglement measures, concurrencies, separability criteria |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
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