Inverse Mellin Transformation of Continuous Singular Value Decomposition: A Route to Holographic Renormalization
arXiv:1607.03552 · doi:10.7566/JPSJ.85.114001
Abstract
We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find the mathematical form of each SVD component by the inverse Mellin transformation as well as the power-law behavior of the SVD spectrum. We find that each SVD component is characterized by the two-point spin correlator with a finite correlation length. Then, the continuous limit of the decomposition index in the SVD corresponds to the inverse of the correlation length. These features strongly suggest that the SVD contains mathematical structure the same as the holographic renormalization.
arXiv comment7 pages, 2 figures
References in corpus (11)
- Entanglement renormalization
- Writing CFT correlation functions as AdS scattering amplitudes
- Theory of finite-entanglement scaling at one-dimensional quantum critical points
- Scaling of entanglement support for Matrix Product States
- A Natural Language for AdS/CFT Correlators
- Towards Feynman rules for Mellin amplitudes in AdS/CFT
- Density Matrix Renormalization Group of Gapless Systems
- Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems
- Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems
- Entropy of Factorized Snapshot Data for Two-Dimensional Classical Spin Models
- Comment on "Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems"