TY - JOUR
T1 - Exact mapping from singular-value spectrum of fractal images to entanglement spectrum of one-dimensional quantum systems
AU - Lee, Ching Hua
AU - Yamada, Yuki
AU - Kumamoto, Tatsuya
AU - Matsueda, Hiroaki
N1 - Publisher Copyright:
© 2015 The Physical Society of Japan.
PY - 2015/1/15
Y1 - 2015/1/15
N2 - 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.
AB - 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.
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U2 - 10.7566/JPSJ.84.013001
DO - 10.7566/JPSJ.84.013001
M3 - Article
AN - SCOPUS:84924955893
VL - 84
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
SN - 0031-9015
IS - 1
M1 - 013001
ER -