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  Towards Complexity for Quantum Field Theory States

Chapman, S., Heller, M. P., Marrochio, H., & Pastawski, F. (2018). Towards Complexity for Quantum Field Theory States. Physical Review Letters, 120(12): 121602. doi:10.1103/PhysRevLett.120.121602.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-DB46-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-E932-F
Genre: Journal Article

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 Creators:
Chapman, Shira, Author
Heller, Michal P.1, Author              
Marrochio, Hugo, Author
Pastawski , Fernando1, Author
Affiliations:
1Gravity, Quantum Fields and Information, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_2477692              

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Free keywords: High Energy Physics - Theory, hep-th,Quantum Physics, quant-ph
 Abstract: We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of Multiscale Entanglement Renormalization Ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum preserving quadratic generators which form $\mathfrak{su}(1,1)$ algebras. On the manifold of Gaussian states generated by these operations the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and holographic complexity proposals.

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 Dates: 2017-07-262018
 Publication Status: Published in print
 Pages: 5+5 pages, 5 appendices, 2 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1707.08582
URI: http://arxiv.org/abs/1707.08582
DOI: 10.1103/PhysRevLett.120.121602
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Title: Physical Review Letters
  Abbreviation : Phys. Rev. Lett.
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. : American Physical Society
Pages: - Volume / Issue: 120 (12) Sequence Number: 121602 Start / End Page: - Identifier: ISSN: 0031-9007
CoNE: /journals/resource/954925433406_1