TY - JOUR

T1 - Inverse mellin transformation of continuous singular value decomposition

T2 - A route to holographic renormalization

AU - Matsueda, Hiroaki

N1 - Funding Information:
HM acknowledges Ching Hua Lee for his helpful comments on the manuscript. This work was supported by JSPS KAKENHI Grant Numbers 15K05222 and 15H03652.
Publisher Copyright:
©2016 The Physical Society of Japan.

PY - 2016/11/15

Y1 - 2016/11/15

N2 - We examine holographic renormalization by singular value decomposition (SVD) of matrix data generated by a Monte Carlo snapshot of the two-dimensional (2D) classical Ising model at criticality. Taking 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 indicate that the SVD contains the same mathematical structure as the holographic renormalization.

AB - We examine holographic renormalization by singular value decomposition (SVD) of matrix data generated by a Monte Carlo snapshot of the two-dimensional (2D) classical Ising model at criticality. Taking 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 indicate that the SVD contains the same mathematical structure as the holographic renormalization.

UR - http://www.scopus.com/inward/record.url?scp=84994772085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994772085&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.85.114001

DO - 10.7566/JPSJ.85.114001

M3 - Article

AN - SCOPUS:84994772085

SN - 0031-9015

VL - 85

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

IS - 11

M1 - 114001

ER -