Exact mapping from singular value spectrum of a class of fractal images to entanglement spectrum of one-dimensional free fermions

Hiroaki Matsueda, Ching Hua Lee

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We examine singular value spectrum of a class of two-dimensional fractal images. We find that the spectra can be mapped onto entanglement spectra of free fermions in one dimension. This exact mapping tells us that the singular value decomposition is a way of detecting a holographic relation between classical and quantum systems.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
EditorsTheodore E. Simos, Theodore E. Simos, Charalambos Tsitouras, Theodore E. Simos
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735412873
DOIs
Publication statusPublished - 2015 Mar 10
Externally publishedYes
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: 2014 Sep 222014 Sep 28

Publication series

NameAIP Conference Proceedings
Volume1648
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
CountryGreece
CityRhodes
Period14/9/2214/9/28

Keywords

  • Area law scaling
  • Entanglement entropy
  • Entanglement spectrum
  • Holography
  • logarithmic violation
  • Ryu-Takayanagi formula
  • Singular Value Decomposition (SVD)
  • Snapshot entropy
  • Suzuki-Trotter decomposition
  • SVD spectrum

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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  • Cite this

    Matsueda, H., & Lee, C. H. (2015). Exact mapping from singular value spectrum of a class of fractal images to entanglement spectrum of one-dimensional free fermions. In T. E. Simos, T. E. Simos, C. Tsitouras, & T. E. Simos (Eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 [200003] (AIP Conference Proceedings; Vol. 1648). American Institute of Physics Inc.. https://doi.org/10.1063/1.4912481