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arXiv · 1403.0163

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
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Abstract

We examine the snapshot entropy of general 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 a holographic interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the Calabrese-Cardy formula. However, the coarse-grained entropy exhibits a linear scaling due to the degeneracy of the spectrum, in contrast with the logarithmic scaling behavior in one-dimensional quantum near-critical systems.

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Ching Hua Lee, Yuki Yamada, Tatsuya Kumamoto, Hiroaki Matsueda. 2014-03-02. Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems. https://doi.org/10.7566/jpsj.84.013001

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