Many-body localization in a quasiperiodic Fibonacci chain

We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance de...

Full description

Saved in:
Bibliographic Details
Published inSciPost physics Vol. 6; no. 4; p. 050
Main Authors Macé, Nicolas, Laflorencie, Nicolas, Alet, Fabien
Format Journal Article
LanguageEnglish
Published SciPost Foundation 01.04.2019
SciPost
Subjects
Condensed Matter
Disordered Systems and Neural Networks
Physics
Online AccessGet full text
ISSN2542-4653
2542-4653
DOI10.21468/SciPostPhys.6.4.050

Cover

Abstract We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.
AbstractList We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.
We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.
ArticleNumber 050
Author Alet, Fabien
Laflorencie, Nicolas
Macé, Nicolas
Author_xml – sequence: 1
  givenname: Nicolas
  surname: Macé
  fullname: Macé, Nicolas
  organization: Laboratoire de Physique Théorique Toulouse
– sequence: 2
  givenname: Nicolas
  surname: Laflorencie
  fullname: Laflorencie, Nicolas
  organization: Laboratoire de Physique Théorique Toulouse
– sequence: 3
  givenname: Fabien
  surname: Alet
  fullname: Alet, Fabien
  organization: Laboratoire de Physique Théorique Toulouse
BackLink https://hal.science/hal-02136475$$DView record in HAL
BookMark eNp9kE1LwzAYx4NMcM59Aw-9emhN0idp620M5wYTB-o5PE1Sl1Gb2Vahfnq7TWF68PS88H-B3zkZVL6yhFwyGnEGMr1-1G7lm3a17ppIRhBRQU_IkAvgIUgRD472MzJumg2llDOWMSmGJLvHqgtzb7qg9BpL94mt81XgqgCDt3ds3NbWzhung5nLfYVau0Cv0VUX5LTAsrHj7zkiz7Pbp-k8XD7cLaaTZahBxm2ISWyokQYRkElgKYtznjLJ891dZCIGiRp5ghR5kYGmVjLoNVpkjGdZPCKLQ67xuFHb2r1i3SmPTu0fvn5RWLdOl1aBTY2geZJAgaBTiVluwaDpq4o8lbLPujpkrbH8FTWfLNXu14OJJSTig_Xam4NW175palso7do9nLZGVypG1Z6_OuKvpALV8-_N8Mf80_av7QtN-o6U
CitedBy_id crossref_primary_10_1103_PhysRevB_106_184208
crossref_primary_10_1103_RevModPhys_97_011001
crossref_primary_10_1088_2633_1357_abaa35
crossref_primary_10_1103_PhysRevB_103_184205
crossref_primary_10_1103_PhysRevB_109_014210
crossref_primary_10_1038_s41534_022_00654_9
crossref_primary_10_1103_PhysRevB_109_134504
crossref_primary_10_1007_s10955_020_02681_2
crossref_primary_10_1103_PhysRevB_102_174205
crossref_primary_10_1103_PhysRevB_104_174203
crossref_primary_10_12677_MP_2023_132006
crossref_primary_10_1103_PhysRevResearch_2_033154
crossref_primary_10_1088_1361_6633_ad9756
crossref_primary_10_1103_PhysRevResearch_5_013083
crossref_primary_10_1103_RevModPhys_94_045006
crossref_primary_10_1103_PhysRevResearch_6_L022054
crossref_primary_10_3390_sym14091780
crossref_primary_10_1103_PhysRevLett_125_156601
crossref_primary_10_1103_PhysRevB_106_144205
crossref_primary_10_1103_PhysRevB_101_064203
crossref_primary_10_1088_1742_5468_ab6de0
crossref_primary_10_1103_PhysRevB_110_184209
crossref_primary_10_21468_SciPostPhysCore_2_2_006
crossref_primary_10_1103_PhysRevB_101_104201
crossref_primary_10_21468_SciPostPhys_12_6_201
crossref_primary_10_1103_PhysRevB_105_045140
crossref_primary_10_1103_PhysRevB_100_085105
crossref_primary_10_1016_j_physleta_2023_128810
crossref_primary_10_1103_PhysRevLett_124_186601
crossref_primary_10_1103_PhysRevB_109_134202
crossref_primary_10_1103_PhysRevB_105_224203
crossref_primary_10_1103_PhysRevB_102_064211
crossref_primary_10_1088_1742_5468_ab6b1b
crossref_primary_10_1103_PhysRevB_104_205411
crossref_primary_10_1103_PhysRevB_102_014310
crossref_primary_10_1103_PhysRevB_103_214206
crossref_primary_10_1103_PhysRevResearch_3_033257
crossref_primary_10_1038_s41567_020_0908_7
crossref_primary_10_1103_PhysRevB_104_214202
crossref_primary_10_1103_PhysRevB_104_214201
crossref_primary_10_1103_RevModPhys_93_045001
crossref_primary_10_1142_S0219749924500473
crossref_primary_10_1088_1751_8121_acc0ec
crossref_primary_10_1103_PhysRevB_100_104203
crossref_primary_10_1103_PhysRevResearch_2_033262
crossref_primary_10_1103_PhysRevB_102_064206
crossref_primary_10_1103_PhysRevB_101_014203
crossref_primary_10_1103_PhysRevB_102_104201
crossref_primary_10_1103_PhysRevB_102_104203
crossref_primary_10_1103_PhysRevB_110_014203
Cites_doi 10.1103/PhysRevB.45.176
10.1088/1742-5468/2013/09/P09005
10.1145/1089014.1089019
10.1103/PhysRevB.82.174411
10.1063/1.531914
10.1103/PhysRevB.75.155111
10.1002/andp.201700169
10.1002/andp.201600326
10.1007/BF01014899
10.1007/3-540-46122-1_18
10.1103/PhysRevA.95.021601
10.1142/S0218348X19500075
10.1103/PhysRevX.5.031033
10.1103/PhysRevB.87.134202
10.1002/andp.201600350
10.1103/PhysRevB.91.161109
10.1103/PhysRevB.65.014201
10.1103/PhysRevLett.73.3379
10.1209/0295-5075/79/37001
10.1103/PhysRevLett.110.260601
10.1103/PhysRevB.77.064426
10.1109/MCSE.2007.55
10.1103/PhysRevA.33.1141
10.1007/BF01044450
10.1088/0022-3727/40/13/R01
10.1103/PhysRevLett.119.260401
10.1103/PhysRevB.93.060201
10.1103/PhysRevB.94.201116
10.1017/CBO9781107326019
10.1103/PhysRevB.98.104203
10.1103/PhysRevE.89.042112
10.1073/pnas.1800589115
10.1103/PhysRevB.94.045111
10.1103/PhysRevB.42.10329
10.21468/SciPostPhys.1.1.010
10.1103/PhysRevB.71.134408
10.1103/PhysRevLett.114.100601
10.1209/0295-5075/119/37003
10.1103/PhysRevLett.109.106402
10.1016/j.crhy.2018.03.003
10.1103/PhysRevLett.95.206603
10.1103/PhysRevLett.110.084101
10.1103/PhysRevLett.73.2607
10.1103/PhysRevA.43.2046
10.1109/IPDPS.2017.21
10.1103/PhysRevB.94.241104
10.1016/j.nuclphysb.2014.12.014
10.1209/0295-5075/2/4/001
10.1103/PhysRevLett.112.146404
10.1103/PhysRevLett.111.127205
10.1103/PhysRevB.96.104205
10.21468/SciPostPhys.5.5.045
10.1103/PhysRevB.90.174202
10.1016/S0370-1573(97)00076-8
10.1103/PhysRevLett.121.206601
10.1103/PhysRevE.96.032130
10.1002/andp.201600356
10.1103/PhysRevLett.117.027201
10.1103/PhysRevB.54.14896
10.1103/PhysRevB.97.155133
10.1016/j.aop.2005.11.014
10.1103/PhysRevA.92.063426
10.1103/PhysRevB.93.075141
10.1103/PhysRevLett.94.077201
10.1103/PhysRevB.97.104406
10.1103/PhysRevLett.71.1291
10.1103/PhysRevLett.119.075702
10.1103/PhysRevX.5.031032
10.1103/PhysRevLett.50.1873
10.1103/PhysRevLett.109.017202
10.1088/0305-4470/33/1/304
10.1103/PhysRevLett.78.2803
10.1103/PhysRevB.99.054203
10.1103/PhysRevB.95.020201
10.1126/science.aaa7432
10.1007/b13861
10.1103/PhysRevLett.77.4752
10.1103/PhysRevB.95.045121
10.1007/BF01127714
10.1103/PhysRevB.98.035118
10.1103/PhysRevB.91.081103
10.1103/PhysRevX.7.021013
10.1103/PhysRevB.35.1020
10.1103/PhysRevLett.113.107204
10.1103/RevModPhys.80.1355
10.1103/PhysRevB.96.060202
10.1103/PhysRevB.96.075146
10.1103/PhysRevE.50.888
10.1103/PhysRevA.60.R4233
10.1103/PhysRevB.80.214203
10.1137/15M1010117
10.1103/PhysRevLett.115.046603
10.1209/0295-5075/24/5/007
10.1103/PhysRevB.96.045138
10.1103/PhysRevLett.83.3908
10.12693/APhysPolA.132.1707
10.1103/PhysRevLett.79.1837
ContentType Journal Article
Copyright Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml – notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID AAYXX
CITATION
1XC
DOA
DOI 10.21468/SciPostPhys.6.4.050
DatabaseName CrossRef
Hyper Article en Ligne (HAL)
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList

CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2542-4653
ExternalDocumentID oai_doaj_org_article_4e8d50b774fa4c86a9be4dadb4afb866
oai_HAL_hal_02136475v1
10_21468_SciPostPhys_6_4_050
GroupedDBID 5VS
AAFWJ
AAYXX
ADBBV
AFPKN
ALMA_UNASSIGNED_HOLDINGS
BCNDV
CITATION
GROUPED_DOAJ
M~E
OK1
1XC
ID FETCH-LOGICAL-c463t-a73d0d6daa4a1641813b28162b4a16f95346aca27a0a2f94c0e6143b2c5912993
IEDL.DBID DOA
ISSN 2542-4653
IngestDate Wed Aug 27 01:29:46 EDT 2025
Fri May 09 12:14:51 EDT 2025
Thu Apr 24 23:00:52 EDT 2025
Tue Jul 01 03:56:31 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 4
Language English
License Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c463t-a73d0d6daa4a1641813b28162b4a16f95346aca27a0a2f94c0e6143b2c5912993
ORCID 0000-0003-0802-6128
0000-0001-8634-1006
0000-0002-2438-7524
OpenAccessLink https://doaj.org/article/4e8d50b774fa4c86a9be4dadb4afb866
ParticipantIDs doaj_primary_oai_doaj_org_article_4e8d50b774fa4c86a9be4dadb4afb866
hal_primary_oai_HAL_hal_02136475v1
crossref_citationtrail_10_21468_SciPostPhys_6_4_050
crossref_primary_10_21468_SciPostPhys_6_4_050
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2019-04-01
PublicationDateYYYYMMDD 2019-04-01
PublicationDate_xml – month: 04
  year: 2019
  text: 2019-04-01
  day: 01
PublicationDecade 2010
PublicationTitle SciPost physics
PublicationYear 2019
Publisher SciPost Foundation
SciPost
Publisher_xml – name: SciPost Foundation
– name: SciPost
References ref57
ref56
ref59
ref58
ref53
ref52
ref55
ref54
ref51
ref50
ref46
ref45
ref48
ref47
ref42
ref41
ref44
ref43
ref49
ref8
ref7
ref9
ref4
ref3
ref6
ref5
ref40
ref35
ref34
ref37
ref36
ref31
ref30
ref33
ref32
ref39
ref38
ref24
ref23
ref26
ref25
ref20
ref22
ref21
ref28
ref27
ref29
ref13
ref12
ref15
ref14
ref97
ref96
ref11
ref10
ref98
ref17
ref16
ref19
ref18
ref93
ref92
ref95
ref94
ref91
ref90
ref89
ref86
ref85
ref88
ref87
ref82
ref81
ref84
ref83
ref80
ref79
ref78
ref75
ref74
ref77
ref76
ref2
ref1
ref71
ref70
ref73
ref72
ref68
ref67
ref69
ref64
ref63
ref66
ref65
ref60
ref62
ref61
References_xml – ident: ref87
  doi: 10.1103/PhysRevB.45.176
– ident: ref54
  doi: 10.1088/1742-5468/2013/09/P09005
– ident: ref95
  doi: 10.1145/1089014.1089019
– ident: ref32
  doi: 10.1103/PhysRevB.82.174411
– ident: ref49
  doi: 10.1063/1.531914
– ident: ref53
  doi: 10.1103/PhysRevB.75.155111
– ident: ref11
  doi: 10.1002/andp.201700169
– ident: ref16
  doi: 10.1002/andp.201600326
– ident: ref86
  doi: 10.1007/BF01014899
– ident: ref50
  doi: 10.1007/3-540-46122-1_18
– ident: ref28
  doi: 10.1103/PhysRevA.95.021601
– ident: ref61
  doi: 10.1142/S0218348X19500075
– ident: ref81
  doi: 10.1103/PhysRevX.5.031033
– ident: ref34
  doi: 10.1103/PhysRevB.87.134202
– ident: ref10
  doi: 10.1002/andp.201600350
– ident: ref18
  doi: 10.1103/PhysRevB.91.161109
– ident: ref21
  doi: 10.1103/PhysRevB.65.014201
– ident: ref78
  doi: 10.1103/PhysRevLett.73.3379
– ident: ref46
  doi: 10.1209/0295-5075/79/37001
– ident: ref76
  doi: 10.1103/PhysRevLett.110.260601
– ident: ref74
  doi: 10.1103/PhysRevB.77.064426
– ident: ref98
  doi: 10.1109/MCSE.2007.55
– ident: ref69
  doi: 10.1103/PhysRevA.33.1141
– ident: ref60
  doi: 10.1007/BF01044450
– ident: ref89
  doi: 10.1088/0022-3727/40/13/R01
– ident: ref71
  doi: 10.1103/PhysRevLett.119.260401
– ident: ref72
  doi: 10.1103/PhysRevB.93.060201
– ident: ref26
  doi: 10.1103/PhysRevB.94.201116
– ident: ref43
  doi: 10.1017/CBO9781107326019
– ident: ref24
  doi: 10.1103/PhysRevB.98.104203
– ident: ref63
  doi: 10.1103/PhysRevE.89.042112
– ident: ref85
  doi: 10.1073/pnas.1800589115
– ident: ref65
  doi: 10.1103/PhysRevB.94.045111
– ident: ref45
  doi: 10.1103/PhysRevB.42.10329
– ident: ref36
  doi: 10.21468/SciPostPhys.1.1.010
– ident: ref23
  doi: 10.1103/PhysRevB.71.134408
– ident: ref82
  doi: 10.1103/PhysRevLett.114.100601
– ident: ref83
  doi: 10.1209/0295-5075/119/37003
– ident: ref90
  doi: 10.1103/PhysRevLett.109.106402
– ident: ref12
  doi: 10.1016/j.crhy.2018.03.003
– ident: ref58
  doi: 10.1103/PhysRevB.75.155111
– ident: ref4
  doi: 10.1103/PhysRevLett.95.206603
– ident: ref59
  doi: 10.1103/PhysRevLett.110.084101
– ident: ref41
  doi: 10.1103/PhysRevLett.73.2607
– ident: ref6
  doi: 10.1103/PhysRevA.43.2046
– ident: ref97
  doi: 10.1109/IPDPS.2017.21
– ident: ref17
  doi: 10.1103/PhysRevB.94.241104
– ident: ref9
  doi: 10.1016/j.nuclphysb.2014.12.014
– ident: ref47
  doi: 10.1209/0295-5075/2/4/001
– ident: ref92
  doi: 10.1103/PhysRevLett.112.146404
– ident: ref73
  doi: 10.1103/PhysRevLett.111.127205
– ident: ref84
  doi: 10.1103/PhysRevB.96.104205
– ident: ref13
  doi: 10.21468/SciPostPhys.5.5.045
– ident: ref64
  doi: 10.1103/PhysRevB.90.174202
– ident: ref77
  doi: 10.1016/S0370-1573(97)00076-8
– ident: ref35
  doi: 10.1103/PhysRevLett.121.206601
– ident: ref51
  doi: 10.1103/PhysRevE.96.032130
– ident: ref42
  doi: 10.1002/andp.201600356
– ident: ref8
  doi: 10.1103/PhysRevLett.117.027201
– ident: ref30
  doi: 10.1103/PhysRevB.54.14896
– ident: ref19
  doi: 10.1103/PhysRevB.97.155133
– ident: ref5
  doi: 10.1016/j.aop.2005.11.014
– ident: ref94
  doi: 10.1103/PhysRevA.92.063426
– ident: ref91
  doi: 10.1103/PhysRevB.93.075141
– ident: ref22
  doi: 10.1103/PhysRevLett.94.077201
– ident: ref68
  doi: 10.1103/PhysRevB.97.104406
– ident: ref56
  doi: 10.1103/PhysRevLett.71.1291
– ident: ref57
  doi: 10.1103/PhysRevLett.119.075702
– ident: ref80
  doi: 10.1103/PhysRevX.5.031032
– ident: ref38
  doi: 10.1103/PhysRevLett.50.1873
– ident: ref75
  doi: 10.1103/PhysRevLett.109.017202
– ident: ref48
  doi: 10.1088/0305-4470/33/1/304
– ident: ref2
  doi: 10.1103/PhysRevLett.78.2803
– ident: ref62
  doi: 10.1103/PhysRevB.99.054203
– ident: ref27
  doi: 10.1103/PhysRevB.95.020201
– ident: ref70
  doi: 10.1126/science.aaa7432
– ident: ref44
  doi: 10.1007/b13861
– ident: ref31
  doi: 10.1103/PhysRevLett.77.4752
– ident: ref25
  doi: 10.1103/PhysRevB.95.045121
– ident: ref39
  doi: 10.1007/BF01127714
– ident: ref15
  doi: 10.1103/PhysRevB.98.035118
– ident: ref33
  doi: 10.1103/PhysRevB.91.081103
– ident: ref14
  doi: 10.1103/PhysRevX.7.021013
– ident: ref40
  doi: 10.1103/PhysRevB.35.1020
– ident: ref55
  doi: 10.1103/PhysRevLett.113.107204
– ident: ref1
  doi: 10.1103/RevModPhys.80.1355
– ident: ref67
  doi: 10.1103/PhysRevB.96.060202
– ident: ref37
  doi: 10.1103/PhysRevB.96.075146
– ident: ref7
  doi: 10.1103/PhysRevE.50.888
– ident: ref93
  doi: 10.1103/PhysRevA.60.R4233
– ident: ref79
  doi: 10.1103/PhysRevB.80.214203
– ident: ref96
  doi: 10.1137/15M1010117
– ident: ref66
  doi: 10.1103/PhysRevLett.115.046603
– ident: ref88
  doi: 10.1209/0295-5075/24/5/007
– ident: ref52
  doi: 10.1103/PhysRevB.96.045138
– ident: ref20
  doi: 10.1103/PhysRevLett.83.3908
– ident: ref29
  doi: 10.12693/APhysPolA.132.1707
– ident: ref3
  doi: 10.1103/PhysRevLett.79.1837
SSID ssj0002119165
Score 2.3489676
Snippet We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting...
We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting...
SourceID doaj
hal
crossref
SourceType Open Website
Open Access Repository
Enrichment Source
Index Database
StartPage 050
SubjectTerms Condensed Matter
Disordered Systems and Neural Networks
Physics
Title Many-body localization in a quasiperiodic Fibonacci chain
URI https://hal.science/hal-02136475
https://doaj.org/article/4e8d50b774fa4c86a9be4dadb4afb866
Volume 6
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF6kIHgRn1hfBPG6bZJ9dPdYxVLEerLQ2zK7SWhAUrWt4L93dpOWeOrFYzaTB99k95sNM98Qcq-V5S5xQBlGq5QrF1PrJFDH_WKIp3LwBc6TVzme8ueZmLVaffmcsFoeuAauz3OVidhilFIAd0qCtjnPILMcCqtkENtGzmttpvwaHHTLpKhr5XzvatXHueL73_rEyp7s8V7sS-1bXBQk-5Fh5ps_qoFhRkfksAkNo2H9SsdkL69OyH5I0XTLU6InOG-pXWQ_USCgpoAyKqsIos81LEsvWrzISheNSosBtnNl5Oa48z8j09HT2-OYNo0PECLJVhQGLIszmQFwwO0MkjCzqUpkav1xoQXjEhykA4ghLTR3cY4sizZOaORvzc5Jp1pU-QWJZKpVbFM08-losYRE5SkTILQYMKl4l7ANBMY1quC-OcW7wd1BAM60gDPScIPAdQndXvVRq2LssH_w6G5tvaZ1GEBPm8bTZpenu-QOffPnHuPhi_Fj6G-vgy--k8v_eNIVOcC4SNcJOteks_pa5zcYe6zsbfjMfgEdn9fx
linkProvider Directory of Open Access Journals
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=Many-body+localization+in+a+quasiperiodic+Fibonacci+chain&rft.jtitle=SciPost+physics&rft.au=Mac%C3%A9%2C+Nicolas&rft.au=Laflorencie%2C+Nicolas&rft.au=Alet%2C+Fabien&rft.date=2019-04-01&rft.issn=2542-4653&rft.eissn=2542-4653&rft.volume=6&rft.issue=4&rft_id=info:doi/10.21468%2FSciPostPhys.6.4.050&rft.externalDBID=n%2Fa&rft.externalDocID=10_21468_SciPostPhys_6_4_050
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2542-4653&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2542-4653&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2542-4653&client=summon