Minimizing couplings in renormalization by preserving short-range mutual information

Abstract The connections between renormalization in statistical mechanics and information theory are intuitively evident, but a satisfactory theoretical treatment remains elusive. We show that the real space renormalization map that minimizes long range couplings in the renormalized Hamiltonian is,...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 55; no. 37; pp. 375004 - 375015
Main Authors Bertoni, Christian, Renes, Joseph M
Format Journal Article
LanguageEnglish
Published IOP Publishing 16.09.2022
Subjects
Markov network
real space mutual information
renormalization
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Summary:Abstract The connections between renormalization in statistical mechanics and information theory are intuitively evident, but a satisfactory theoretical treatment remains elusive. We show that the real space renormalization map that minimizes long range couplings in the renormalized Hamiltonian is, somewhat counterintuitively, the one that minimizes the loss of short-range mutual information between a block and its boundary. Moreover, we show that a previously proposed minimization focusing on preserving long-range mutual information is a relaxation of this approach, which indicates that the aims of preserving long-range physics and eliminating short-range couplings are related in a nontrivial way.
Bibliography:JPhysA-117434.R2
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ac8383