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.
REFERENCES
1.
Masuo
Suzuki
, Prog. Theor. Phys.
56
, 1454
(1976
).2.
3.
Guifre
Vidal
, Phys. Rev. Lett.
99
, 220405
(2007
).4.
Hiroaki
Matsueda
, Phys. Rev. E
85
, 031101
(2012
).5.
Yukinari
Imura
, Tsuyoshi
Okubo
, Satoshi
Morita
, and Kouichi
Okunishi
, J. Phys. Soc. Jpn.
83
, 114002
(2014
).6.
7.
8.
9.
Ingo
Peschel
, J. Phys. A: Math. Gen.
36
, L205
(2003
).10.
Christoph
Holzhey
, Finn
Larsen
, and Frank
Wilczek
, Nucl. Phys. B
424
, 443
(1994
).11.
Pasquale
Calabrese
and John
Cardy
, J. Stat. Mech.
0406
, P002
(2004
).12.
Shinsei
Ryu
and Tadashi
Takayanagi
, Phys. Rev. Lett.
96
, 181602
(2006
).
This content is only available via PDF.
© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.
