August 4th-7th, 2014
Yukawa Institute for Theoretical Physics, Kyoto University
"Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems"
Hiroaki Matsueda (SNCT)
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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