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Identification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning

hal.structure.identifierArnold Sommerfeld Center for Theoretical Physics [München] [ASC]
hal.structure.identifierMunich Center for Quantum Science and Technology [MCQST]
dc.contributor.authorGREITEMANN, Jonas
hal.structure.identifierArnold Sommerfeld Center for Theoretical Physics [München] [ASC]
hal.structure.identifierMunich Center for Quantum Science and Technology [MCQST]
dc.contributor.authorLIU, Ke
hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorJAUBERT, L.D.C.
hal.structure.identifierOkinawa Institute of Science and Technology Graduate University [OIST]
dc.contributor.authorYAN, Han
hal.structure.identifierOkinawa Institute of Science and Technology Graduate University [OIST]
dc.contributor.authorSHANNON, Nic
hal.structure.identifierArnold Sommerfeld Center for Theoretical Physics [München] [ASC]
hal.structure.identifierMunich Center for Quantum Science and Technology [MCQST]
hal.structure.identifierWilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University
dc.contributor.authorPOLLET, Lode
dc.date.issued2019-11-05
dc.identifier.issn1098-0121
dc.description.abstractEnMachine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine-learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter tensors of phases with broken symmetry, and the local constraints which signal an emergent gauge structure, and so characterize classical spin liquids. The method is applied to the classical XXZ model on the pyrochlore lattice where it distinguishes, among others, between a hidden biaxial spin-nematic phase and several different classical spin liquids. The results are in full agreement with a previous analysis by Taillefumier et al. [Phys. Rev. X 7, 041057 (2017)], but go further by providing a systematic hierarchy between disordered regimes, and establishing the physical relevance of the susceptibilities associated with the local constraints. Our work paves the way for the search of new orders and spin liquids in generic frustrated magnets.
dc.description.sponsorshipDesign de la frustration: effets de surface et désordre - ANR-18-CE30-0011
dc.language.isoen
dc.publisherAmerican Physical Society
dc.title.enIdentification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning
dc.typeArticle de revue
dc.identifier.doi10.1103/PhysRevB.100.174408
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Electrons fortement corrélés [cond-mat.str-el]
dc.subject.halPhysique [physics]/Physique [physics]/Physique Numérique [physics.comp-ph]
dc.identifier.arxiv1907.12322
dc.description.sponsorshipEuropeFP7/ERC Consolidator Grant QSIMCORR, No. 771891
bordeaux.journalPhysical Review B: Condensed Matter and Materials Physics (1998-2015)
bordeaux.page174408
bordeaux.volume100
bordeaux.peerReviewedoui
hal.identifierhal-02265929
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02265929v1
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