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

doi:10.1063/1.4912481

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

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Editors	Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras, Theodore E. Simos
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735412873
DOIs	https://doi.org/10.1063/1.4912481
Publication status	Published - 2015 Mar 10
Externally published	Yes
Event	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece Duration: 2014 Sep 22 → 2014 Sep 28

Publication series

Name	AIP Conference Proceedings
Volume	1648
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Country	Greece
City	Rhodes
Period	14/9/22 → 14/9/28

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)

Access to Document

10.1063/1.4912481

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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

Exact mapping from singular value spectrum of a class of fractal images to entanglement spectrum of one-dimensional free fermions. / Matsueda, Hiroaki; Lee, Ching Hua.

Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. ed. / Theodore E. Simos; Theodore E. Simos; Charalambos Tsitouras; Theodore E. Simos. American Institute of Physics Inc., 2015. 200003 (AIP Conference Proceedings; Vol. 1648).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Matsueda, H & Lee, CH 2015, Exact mapping from singular value spectrum of a class of fractal images to entanglement spectrum of one-dimensional free fermions. in TE Simos, TE Simos, C Tsitouras & TE 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., International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014, Rhodes, Greece, 14/9/22. https://doi.org/10.1063/1.4912481

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

Matsueda, Hiroaki ; Lee, Ching Hua. / Exact mapping from singular value spectrum of a class of fractal images to entanglement spectrum of one-dimensional free fermions. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. editor / Theodore E. Simos ; Theodore E. Simos ; Charalambos Tsitouras ; Theodore E. Simos. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

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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",

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