Information Geometry and the Renormalization Group

Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality, for both classi...

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Published in:arXiv.org 2015-10
Main Authors: Maity, Reevu, Mahapatra, Subhash, Sarkar, Tapobrata
Format: Article
Language:English
Subjects:
Critical point
Curvature
Flow equations
Geometry
Information theory
Parameter identification
Scaling
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Mahapatra, Subhash
Sarkar, Tapobrata
description Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality, for both classical and quantum systems, in an universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.
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subjects Critical point
Curvature
Flow equations
Geometry
Information theory
Parameter identification
Scaling
title Information Geometry and the Renormalization Group
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