[Seminar] “Singular-Value-Decomposition Analysis of Holography and Renormalization Group” - by Prof. Hiroaki Matsueda, NIT Sendai
Speaker: Prof. Hiroaki Matsueda
Vice President (Advanced Course) in National Institute of Technology, Sendai College
We examine holography and renormalization group by singular value decomposition (SVD) of matrix data generated by a Monte Carlo snapshot of the two-dimensional classical ferromagnetic Ising model at criticality. SVD is a way of principle-component analysis in information science, and recently physicists are becoming aware that SVD also plays central roles in various branches of theoretical physics. In the present case, the SVD enables us to extract essential information of critical phenomena and quantum-classical correspondence inherent in this model. Thus, the SVD provides us with a new way of examination of holography and renormalization group. The snapshot entropy defined from the SVD spectra is a key quantity, and it behaves like the holographic entanglement entropy. This unique character of the entropy originates from a fact that the decomposition index in the SVD corresponds to the inverse correlation length. The results strongly indicate that the SVD contains the same mathematical structure as the holographic renormalization developed in the superstring theory.