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,...

Full description

Saved in:
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
Online AccessGet full text

Cover

Abstract 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.
AbstractList 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.
Author Bertoni, Christian
Renes, Joseph M
Author_xml – sequence: 1
  givenname: Christian
  orcidid: 0000-0001-7715-4591
  surname: Bertoni
  fullname: Bertoni, Christian
  organization: Freie Universität Berlin Dahlem Center for Complex Quantum Systems, Germany
– sequence: 2
  givenname: Joseph M
  orcidid: 0000-0003-2302-8025
  surname: Renes
  fullname: Renes, Joseph M
  organization: Institute for Theoretical Physics , ETH Zürich, Switzerland
BookMark eNp9kE1rwzAMhs3oYG23-4457bSs_ogT-zjKvqBjl-5sHMfuXBI72Mmg_fVz6OhpDAQS0vMK6V2AmfNOA3CL4AOCjK1QRVHOEEYrqRhh5ALMz63ZuUbkCixi3ENIC8jxHGzfrbOdPVq3y5Qf-zYVMbMuC9r50MnWHuVgvcvqQ9YHHXX4ntD45cOQB-l2OuvGYZRt0phJMMHX4NLINuqb37wEn89P2_Vrvvl4eVs_bnJFYDnkVdFwhMvKSIUVrDkvGeGoMjU3TdGUGpdpSKmucY0wU7wkTc1YYxrDi4QxsgTwtFcFH2PQRvTBdjIcBIJickVMb4vJAnFyJUnuTxLre7H3Y3DpwP_wuz9wKSgVpEpBISxE3xjyAxEuc0w
CODEN JPHAC5
Cites_doi 10.1126/science.1238723
10.1103/physrevlett.99.120601
10.1103/physrevlett.115.180405
10.1103/revmodphys.47.773
10.1103/physrevx.10.011037
10.1103/PhysRevLett.127.240603
10.1038/s41567-018-0081-4
10.1016/j.physa.2011.08.014
10.2307/2311462
10.1103/physrevlett.118.250602
10.1103/physrevd.54.5163
10.1103/PhysRevE.104.064106
10.1016/0370-1573(74)90023-4
10.1103/physreva.92.022330
10.1103/PhysicsPhysiqueFizika.2.263
10.1103/physrevb.20.2080
10.1103/physrevlett.81.3587
10.1088/1367-2630/17/8/083005
10.1007/s10701-018-0143-6
10.1143/jpsj.65.891
ContentType Journal Article
Copyright 2022 The Author(s). Published by IOP Publishing Ltd
Copyright_xml – notice: 2022 The Author(s). Published by IOP Publishing Ltd
DBID O3W
TSCCA
AAYXX
CITATION
DOI 10.1088/1751-8121/ac8383
DatabaseName Institute of Physics Open Access Journal Titles
IOPscience (Open Access)
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: O3W
  name: Institute of Physics Open Access Journal Titles
  url: http://iopscience.iop.org/
  sourceTypes:
    Enrichment Source
    Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 1751-8121
ExternalDocumentID 10_1088_1751_8121_ac8383
aac8383
GrantInformation_xml – fundername: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
  funderid: https://doi.org/10.13039/501100001711
– fundername: Deutsche Forschungsgemeinschaft
  grantid: CRC18
  funderid: https://doi.org/10.13039/501100001659
GroupedDBID 1JI
4.4
5B3
5GY
5VS
5ZH
7.M
7.Q
AAGCD
AAGID
AAJIO
AAJKP
AATNI
ABCXL
ABHWH
ABQJV
ABVAM
ACAFW
ACGFS
ACHIP
ACNCT
AEFHF
AFYNE
AKPSB
ALMA_UNASSIGNED_HOLDINGS
AOAED
ASPBG
ATQHT
AVWKF
AZFZN
CBCFC
CEBXE
CJUJL
CRLBU
CS3
EBS
EDWGO
EMSAF
EPQRW
EQZZN
HAK
IHE
IJHAN
IOP
IZVLO
KOT
LAP
M45
N5L
O3W
PJBAE
RIN
RNS
RO9
ROL
RPA
SY9
TN5
TSCCA
W28
AAYXX
CITATION
ID FETCH-LOGICAL-c306t-74d91267fac2c0b99683917fb9fd4d6e2626755eb2b128c963db88dfdf9417f83
IEDL.DBID O3W
ISSN 1751-8113
IngestDate Fri Aug 23 03:49:06 EDT 2024
Wed Aug 21 03:33:31 EDT 2024
Tue Aug 23 23:25:22 EDT 2022
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 37
Language English
License Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c306t-74d91267fac2c0b99683917fb9fd4d6e2626755eb2b128c963db88dfdf9417f83
Notes JPhysA-117434.R2
ORCID 0000-0001-7715-4591
0000-0003-2302-8025
OpenAccessLink https://iopscience.iop.org/article/10.1088/1751-8121/ac8383
PageCount 12
ParticipantIDs crossref_primary_10_1088_1751_8121_ac8383
iop_journals_10_1088_1751_8121_ac8383
PublicationCentury 2000
PublicationDate 2022-09-16
PublicationDateYYYYMMDD 2022-09-16
PublicationDate_xml – month: 09
  year: 2022
  text: 2022-09-16
  day: 16
PublicationDecade 2020
PublicationTitle Journal of physics. A, Mathematical and theoretical
PublicationTitleAbbrev JPhysA
PublicationTitleAlternate J. Phys. A: Math. Theor
PublicationYear 2022
Publisher IOP Publishing
Publisher_xml – name: IOP Publishing
References Wilson (aac8383bib2) 1975; 47
Davis (aac8383bib21) 1961; 68
Li (aac8383bib18) 2018; 48
Levin (aac8383bib23) 2007; 99
Bény (aac8383bib6) 2013
Rockafellar (aac8383bib20) 1970
Bény (aac8383bib7) 2015; 17
Wilson (aac8383bib1) 1974; 12
Swendsen (aac8383bib11) 1979; 20
Evenbly (aac8383bib24) 2015; 115
Gaite (aac8383bib3) 1996; 54
Gökmen (aac8383bib14) 2021
Nishino (aac8383bib22) 1996; 65
Kadanoff (aac8383bib10) 1966; 2
Hammersley (aac8383bib16) 1971
Lenggenhager (aac8383bib13) 2020; 10
Machta (aac8383bib9) 2013; 342
aac8383bib19
Bény (aac8383bib8) 2015; 92
Koller (aac8383bib17) 2009
Apenko (aac8383bib5) 2012; 391
Gaite (aac8383bib4) 1998; 81
Koch-Janusz (aac8383bib12) 2018; 14
Gökmen (aac8383bib15) 2021
Bal (aac8383bib25) 2017; 118
References_xml – year: 1970
  ident: aac8383bib20
  contributor:
    fullname: Rockafellar
– volume: 342
  start-page: 604
  year: 2013
  ident: aac8383bib9
  article-title: Parameter space compression underlies emergent theories and predictive models
  publication-title: Science
  doi: 10.1126/science.1238723
  contributor:
    fullname: Machta
– ident: aac8383bib19
– year: 2013
  ident: aac8383bib6
  article-title: Renormalisation as an inference problem
  contributor:
    fullname: Bény
– volume: 99
  year: 2007
  ident: aac8383bib23
  article-title: Tensor renormalization group approach to two-dimensional classical lattice models
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/physrevlett.99.120601
  contributor:
    fullname: Levin
– volume: 115
  year: 2015
  ident: aac8383bib24
  article-title: Tensor network renormalization
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/physrevlett.115.180405
  contributor:
    fullname: Evenbly
– volume: 47
  start-page: 773
  year: 1975
  ident: aac8383bib2
  article-title: The renormalization group: critical phenomena and the Kondo problem
  publication-title: Rev. Mod. Phys.
  doi: 10.1103/revmodphys.47.773
  contributor:
    fullname: Wilson
– volume: 10
  year: 2020
  ident: aac8383bib13
  article-title: Optimal renormalization group transformation from information theory
  publication-title: Phys. Rev. X
  doi: 10.1103/physrevx.10.011037
  contributor:
    fullname: Lenggenhager
– year: 2021
  ident: aac8383bib14
  article-title: Statistical physics through the lens of real-space mutual information
  doi: 10.1103/PhysRevLett.127.240603
  contributor:
    fullname: Gökmen
– year: 2009
  ident: aac8383bib17
  contributor:
    fullname: Koller
– volume: 14
  start-page: 578
  year: 2018
  ident: aac8383bib12
  article-title: Mutual information, neural networks and the renormalization group
  publication-title: Nat. Phys.
  doi: 10.1038/s41567-018-0081-4
  contributor:
    fullname: Koch-Janusz
– volume: 391
  start-page: 62
  year: 2012
  ident: aac8383bib5
  article-title: Information theory and renormalization group flows
  publication-title: Physica A
  doi: 10.1016/j.physa.2011.08.014
  contributor:
    fullname: Apenko
– volume: 68
  start-page: 264
  year: 1961
  ident: aac8383bib21
  article-title: Markov chains as random input automata
  publication-title: Am. Math. Mon.
  doi: 10.2307/2311462
  contributor:
    fullname: Davis
– volume: 118
  year: 2017
  ident: aac8383bib25
  article-title: Renormalization group flows of Hamiltonians using tensor networks
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/physrevlett.118.250602
  contributor:
    fullname: Bal
– volume: 54
  start-page: 5163
  year: 1996
  ident: aac8383bib3
  article-title: Field theory entropy, the h theorem, and the renormalization group
  publication-title: Phys. Rev. D
  doi: 10.1103/physrevd.54.5163
  contributor:
    fullname: Gaite
– year: 2021
  ident: aac8383bib15
  article-title: Phase diagrams with real-space mutual information neural estimation
  doi: 10.1103/PhysRevE.104.064106
  contributor:
    fullname: Gökmen
– volume: 12
  start-page: 75
  year: 1974
  ident: aac8383bib1
  article-title: The renormalization group and the ε expansion
  publication-title: Phys. Rep.
  doi: 10.1016/0370-1573(74)90023-4
  contributor:
    fullname: Wilson
– volume: 92
  year: 2015
  ident: aac8383bib8
  article-title: Information-geometric approach to the renormalization group
  publication-title: Phys. Rev. A
  doi: 10.1103/physreva.92.022330
  contributor:
    fullname: Bény
– year: 1971
  ident: aac8383bib16
  contributor:
    fullname: Hammersley
– volume: 2
  start-page: 263
  year: 1966
  ident: aac8383bib10
  article-title: Scaling laws for ising models near T c
  publication-title: Phys. Phys. Fiz.
  doi: 10.1103/PhysicsPhysiqueFizika.2.263
  contributor:
    fullname: Kadanoff
– volume: 20
  start-page: 2080
  year: 1979
  ident: aac8383bib11
  article-title: Monte Carlo renormalization-group studies of the d = 2 Ising model
  publication-title: Phys. Rev. B
  doi: 10.1103/physrevb.20.2080
  contributor:
    fullname: Swendsen
– volume: 81
  start-page: 3587
  year: 1998
  ident: aac8383bib4
  article-title: Relative entropy in 2d quantum field theory, finite-size corrections, and irreversibility of the renormalization group
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/physrevlett.81.3587
  contributor:
    fullname: Gaite
– volume: 17
  year: 2015
  ident: aac8383bib7
  article-title: The renormalization group via statistical inference
  publication-title: New J. Phys.
  doi: 10.1088/1367-2630/17/8/083005
  contributor:
    fullname: Bény
– volume: 48
  start-page: 910
  year: 2018
  ident: aac8383bib18
  article-title: Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
  publication-title: Found. Phys.
  doi: 10.1007/s10701-018-0143-6
  contributor:
    fullname: Li
– volume: 65
  start-page: 891
  year: 1996
  ident: aac8383bib22
  article-title: Corner transfer matrix renormalization group method
  publication-title: J. Phys. Soc. Japan
  doi: 10.1143/jpsj.65.891
  contributor:
    fullname: Nishino
SSID ssj0054092
Score 2.4264483
Snippet Abstract The connections between renormalization in statistical mechanics and information theory are intuitively evident, but a satisfactory theoretical...
SourceID crossref
iop
SourceType Aggregation Database
Enrichment Source
Publisher
StartPage 375004
SubjectTerms Markov network
real space mutual information
renormalization
Title Minimizing couplings in renormalization by preserving short-range mutual information
URI https://iopscience.iop.org/article/10.1088/1751-8121/ac8383
Volume 55
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LS8NAEF7aiuBFfGJ91D3owUNsN8kmGzyJWKpQ66HF3pZ9ZDVg09K0B_31ziZbsSAi5JDDsAnDzn7fsPPNIHShEtMRRFvZLzNeSJj2pKCxR1UghCLCsMTqnftPUW8UPo7puIZuvrUw05k7-q_htWoUXLnQFcSxNgAe8QCXSFsoBglWHW0A6vq2nm8QvKyOYWAi5URkZ00Cd0f52wprmFSH7_6AmO4O2nbcEN9Wf7KLamm-hzbLGk1V7KNhP8uzSfYJYIPVdGmltK8FznI8T3PLPN-dpBLLD2zLW-0pAKbFGzBsb25FBHiytHIR7LqlWuMDNOreD-96nhuK4Clg9wsvDnVC_Cg2QvmqIyFdAYpDYiMTo0MdpT5kKDGlkDBLgB4F8aUlY9pok4RgxoJD1MineXqEMDWKqNSmqVKHduB83FGSijRiAjg3M010tXILn1W9L3h5Z80Yty7k1oW8cmETXYLfuAuA4g-78zU7wSnlQQwPhXDlM22O_7nSCdryrRTBjnOITlFjMV-mZ0AQFrKF6g-D51a5Hb4Aw3-04g
link.rule.ids 315,786,790,27957,27958,38900,38925,53877,53903
linkProvider IOP Publishing
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV07T8MwELagCMSCeIryqgcYGELrJE6cEQFVebQwtKKb5UcMkWhaNe0Av55z4kpUQggpQ4aLE118d9_J990hdK4S0xJEW9ovM15ImPakoLFHVSCEIsKwxPKdu72oMwgfhnTo5pyWXJjxxLn-K7itGgVXKnQFcawJAY94EJdIUygGCVZzos0qWqOQvduN_hy8LlwxoJFyKrJ7ggTunPK3VZbi0iq8-0eYaW-jLYcP8XX1NTtoJc130XpZp6mKPdTvZnk2yr4g4GA1nls67VuBsxxP09yizw9Hq8TyE9sSV-sJQLR4B5TtTS2RAI_mljKCXcdUK7yPBu27_k3Hc4MRPAUIf-bFoU6IH8VGKF-1JKQsAHNIbGRidKij1IcsJaYUkmYJ4UeBjWnJmDbaJCGIseAA1fJxnh4iTI0iKrWpqtShHToft5SkIo2YANzNTB1dLtTCJ1X_C16eWzPGrQq5VSGvVFhHF6A37oyg-EOusSQnOKU8iOGiYLIcfufRP1dqoI2X2zZ_uu89HqNN3zIT7HSH6ATVZtN5egp4YSbPyj3xDdpot80
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Minimizing+couplings+in+renormalization+by+preserving+short-range+mutual+information&rft.jtitle=Journal+of+physics.+A%2C+Mathematical+and+theoretical&rft.au=Bertoni%2C+Christian&rft.au=Renes%2C+Joseph+M&rft.date=2022-09-16&rft.issn=1751-8113&rft.eissn=1751-8121&rft.volume=55&rft.issue=37&rft.spage=375004&rft_id=info:doi/10.1088%2F1751-8121%2Fac8383&rft.externalDBID=n%2Fa&rft.externalDocID=10_1088_1751_8121_ac8383
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1751-8113&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1751-8113&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1751-8113&client=summon