Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems

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.

5 pages, 3 figures

References in corpus (2)

• Entanglement spectrum in one-dimensional systems
• Scaling of entanglement support for Matrix Product States

Cited by in corpus (5)

• Singular-Value-Decomposition Analysis of Associative Memory in a Neural Network
• Random Fractal Ansatz for the configurations of Two-Dimensional Critical Systems
• Inverse Mellin Transformation of Continuous Singular Value Decomposition: A Route to Holographic Renormalization
• Exact Mappings in Condensed Matter Physics
• Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model