de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity
Abstract
Here, we investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). Furthermore, we suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti–de Sitter space.
- Authors:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1597496
- Alternate Identifier(s):
- OSTI ID: 1416433
- Grant/Contract Number:
- SC0011632
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 12; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Bao, Ning, Cao, ChunJun, Carroll, Sean M., and Chatwin-Davies, Aidan. de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.123536.
Bao, Ning, Cao, ChunJun, Carroll, Sean M., & Chatwin-Davies, Aidan. de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity. United States. https://doi.org/10.1103/PhysRevD.96.123536
Bao, Ning, Cao, ChunJun, Carroll, Sean M., and Chatwin-Davies, Aidan. Fri .
"de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity". United States. https://doi.org/10.1103/PhysRevD.96.123536. https://www.osti.gov/servlets/purl/1597496.
@article{osti_1597496,
title = {de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity},
author = {Bao, Ning and Cao, ChunJun and Carroll, Sean M. and Chatwin-Davies, Aidan},
abstractNote = {Here, we investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). Furthermore, we suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti–de Sitter space.},
doi = {10.1103/PhysRevD.96.123536},
journal = {Physical Review D},
number = 12,
volume = 96,
place = {United States},
year = {Fri Dec 29 00:00:00 EST 2017},
month = {Fri Dec 29 00:00:00 EST 2017}
}
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