Exact mapping from singular-value spectrum of fractal images to entanglement spectrum of one-dimensional quantum systems

Ching Hua Lee, Yuki Yamada, Tatsuya Kumamoto, Hiroaki Matsueda

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We examine the snapshot entropy of fractal images defined by their singular values. Remarkably, the singular values for a large class of fractals are in exact correspondence with the entanglement spectrum of free fermions in one dimension. These fermions allow for an interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the logarithmic violation formula of the area law scaling. However, the coarse-grained entropy exhibits a linear scaling owing to the degeneracy of the spectrum, in contrast with the logarithmic scaling behavior in onedimensional quantum near-critical systems.

Original languageEnglish
Article number013001
Journaljournal of the physical society of japan
Volume84
Issue number1
DOIs
Publication statusPublished - 2015 Jan 15
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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