[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126819-en":3,"doc-seo-126819-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},126819,1099523885074,"Ivy","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",8,"Research & Report","Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model - Abstract","The study investigates the critical properties of the Ising-Higgs gauge theory in (2+1)D along the self-dual line, where low-energy operator content has been debated. Using machine learning methods, the work determines the operator spectrum of the associated field theory for the first time, enabling strong refutation of an emergent current operator. It contrasts these findings with the (2+1)D Ashkin-Teller transverse field Ising model, where the expected current operator is found, and introduces an extension of Real-Space Mutual Information to extract sub-leading non-linear operators.","arXiv :2311 . 17994v1 [ cond-mat .str-el ] 29 Nov 2023  \nMachine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge  \nModel  \nLior Oppenheim, 1 Maciej Koch-Janusz,2, 3, 4 Snir Gazit, 1, 5 and Zohar Ringel 1  \n1 The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel  \n2 Department of Physics, University of Zurich, 8057 Zurich, Switzerland  \n3 James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA  \n4 Haiqu Inc. , 95 Third Street, San Francisco, California 94103, USA  \n5 The Fritz Haber Research Center for Molecular Dynamics,  \nThe Hebrew University of Jerusalem, Jerusalem 91904, Israel  \nWe study the critical properties of the Ising-Higgs gauge theory in (2+1)D along the self-dual line which have recently been a subject of debate. For the first time, using machine learning techniques, we determine the low energy operator content of the associated field theory. Our approach enables us to largely refute the existence of an emergent current operator and with it the standing conjecture that this transition is of the XY ∗ universality class. We contrast these results with the ones obtained for the (2 + 1)D Ashkin-Teller transverse field Ising model where we find the expected current operator. Our numerical technique extends the recently proposed Real-Space Mutual Information allowing us to extract sub-leading non-linear operators. This allows a controlled and computationally scalable approach to target the CFT spectrum and discern universality classes beyond (1+1)D from Monte Carlo data.  \nIntroduction - The hallmark of critical phenomena is the emergence of a universal behavior governing the longwave-length theory. In this limit, dynamics are often controlled by collective degrees of freedom dictated solely by symmetry and dimensionality. A case in point is symmetry-breaking transitions, whose critical fluctuations are governed by an order parameter directed along the symmetry-breaking axis [1] .  \nA major challenge in modern condensed matter theory is addressing critical phenomena beyond the above Landau paradigm [2, 3] . This includes spin liquids [4], fractional Hall effect [5], and symmetry protected topological transitions [6, 7] . In such cases, identifying the low-energy theory often becomes a formidable task, due to the absence of clear symmetry-based candidates for the low-lying degrees of freedom [8–11] .  \nLattice gauge theories provide a paradigm for studying such criticalities. In this setting, the transition is described by a condensation of gauge field fluxes, charged matter fields, or both. The former is known as the confinement transition, and the latter as the Higgs transition. In their seminal work, Fradkin and Shankar provided a unified framework describing both transitions [12] . Nevertheless, the case in which both transitions occur simultaneously at a multicritical point (MCP) remained elusive.  \nThis outstanding problem attracted much recent interest, particularly the case of the Self-Dual Ising-Higgs Gauge theory in (2 + 1)D (“SD-IHG”)[13–21] . Here the two transitions meeting at the MCP are of the 3D Ising and Ising* universality classes. Following the general insight that MCPs of two Ising transitions may lead to an enhanced U(1) symmetry Bonati et al. [20] argued, with supporting Monte Carlo results, that the emergent theory is of the XY ∗ type [22]—an XY transition exhibiting only gauge invariant operators. However, in the absence of a direct identification of low energy degrees of freedom  \nin terms of the microscopic ones, the validity of such a phenomenological description is unclear.  \nThe ideal way to indisputably verify this conjecture is to obtain the operator spectrum of the theory, or at least its leading orders. Indeed, the putative XY ∗ transition should contain a smoking gun: three degenerate operators with scaling dimension 2, namely the three vector components of the current operator associated with the ","cbCaicUjfbTgYpQr","https://ap.wps.com/l/cbCaicUjfbTgYpQr","pdf",3054114,1,9,"English","en",105,"# Introduction\n## Critical phenomena beyond the Landau paradigm\n## Multicritical points in Ising-Higgs gauge theories\n## Emergent U(1) symmetry and the XY* conjecture\n# Methods and Models\n## Real-Space Mutual Information Neural Estimator (RSMI-NE)\n## SD-IHG and AT-TFI comparative study\n# Results and Conclusions\n## Extraction of leading and sub-leading operators\n## Absence of a local current operator in SD-IHG\n## Implications for universality classification","[{\"question\":\"What is the main goal of the study on the SD-IHG model?\",\"answer\":\"The study aims to determine the low-energy operator content of the critical Ising-Higgs gauge theory along the self-dual line using machine learning techniques.\"},{\"question\":\"How do the authors test the XY* universality conjecture?\",\"answer\":\"They search for a current operator signature expected in an emergent U(1) scenario, focusing on operator degeneracies and scaling dimensions, and then compare with a related model where the current operator is expected.\"},{\"question\":\"Which method is extended to extract sub-leading operators?\",\"answer\":\"The authors extend the Real-Space Mutual Information Neural Estimator (RSMI-NE) to systematically extract sub-leading non-linear operators from Monte Carlo data.\"}]","Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model - Abstract | PDF",1785934981,23,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-the-operator-content-of-the-critical-self-dual-ising-higgs-gauge-model-abstract","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-the-operator-content-of-the-critical-self-dual-ising-higgs-gauge-model-abstract/126819/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of the study on the SD-IHG model?","Question",{"text":75,"@type":76},"The study aims to determine the low-energy operator content of the critical Ising-Higgs gauge theory along the self-dual line using machine learning techniques.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do the authors test the XY* universality conjecture?",{"text":80,"@type":76},"They search for a current operator signature expected in an emergent U(1) scenario, focusing on operator degeneracies and scaling dimensions, and then compare with a related model where the current operator is expected.",{"name":82,"@type":73,"acceptedAnswer":83},"Which method is extended to extract sub-leading operators?",{"text":84,"@type":76},"The authors extend the Real-Space Mutual Information Neural Estimator (RSMI-NE) to systematically extract sub-leading non-linear operators from Monte Carlo data.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]