[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117987-en":3,"doc-seo-117987-105":29,"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":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},117987,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Machine learning the Kondo entanglement cloud from local measurements","A quantum coherent screening cloud around a magnetic impurity defines the antiferromagnetic Kondo effect, yet the real-space structure of its quantum correlations has remained difficult to observe directly. This work presents a machine-learning algorithm that spatially maps entangled electronic modes using experimentally accessible local data. Local correlators reconstruct the local many-body correlation entropy density in a double-Kondo setup with overlapping entanglement clouds. The approach avoids measuring long-range non-local correlators, transfers across different Kondo system sizes, and remains robust under noisy correlators.","arXiv :2311 .07253v2 [ cond-mat .str-el ] 8 May 2024  \nMachine learning the Kondo entanglement cloud from local measurements  \nFaluke Aikebaier, 1, 2, 3 Teemu Ojanen,2, 3 and Jose L. Lado 1  \n1 Department of Applied Physics, Aalto University, 00076, Espoo, Finland  \n2 Computational Physics Laboratory, Physics Unit,  \nFaculty of Engineering and Natural Sciences, Tampere University, FI-33014 Tampere, Finland  \n3 Helsinki Institute of Physics P. O. Box 64, FI-00014, Finland  \nA quantum coherent screening cloud around a magnetic impurity in metallic systems is the hallmark of the antiferromagnetic Kondo effect. Despite the central role of the Kondo effect in quantum materials, the structure of quantum correlations of the screening cloud has defied direct observations. In this work, we introduce a machine-learning algorithm that allows to spatially map the entangled electronic modes in the vicinity of the impurity site from experimentally accessible data. We demonstrate that local correlators allow reconstructing the local many-body correlation entropy in real-space in a double Kondo system with overlapping entanglement clouds. Our machine learning methodology allows bypassing the typical requirement of measuring long-range non-local correlators with conventional methods. We show that our machine learning algorithm is transferable between different Kondo system sizes, and we show its robustness in the presence of noisy correlators. Our work establishes the potential of machine learning methods to map many-body entanglement from real-space measurements.  \nI. INTRODUCTION  \nStrongly interacting quantum many-body systems exhibit a wealth of intricate physical phenomena. Quantum impurity problems, and in particular the Kondo problem [1–3], play a crucial role in capturing properties of the localized interactions within a larger quantum system [4–6] . Such systems provide a paradigmatic framework for understanding the correlation effects and related entanglement features in many-body systems [7–10] . A hallmark feature of the Kondo effect is the formation of a dynamic cloud of conduction electrons, or ”the Kondo screening cloud”, surrounding the impurity. The Kondo cloud, which plays a crucial role in understanding the Kondo problem [11], leads to electron entanglement atmesoscopic scales [12, 13] . Recent experiments have directly confirmed the existence of the Kondo screening cloud [14], however, the detailed structure of the quantum many-body correlations remains elusive. Correlation effects are essential for understanding the emergence of the Kondo effect and the subsequent formation of the Kondo screening cloud [12, 15–18], motivating the development of more powerful strategies to imaging the Kondo entanglement cloud.  \nEntanglement properties of quantum materials are remarkably challenging to extract in experiments. From a theory perspective, correlations in electronic systems can be quantified by means of the von Neumann entropy obtained from one-particle density matrix, known as the correlation entropy [19–24], a quantity that vanishes for any non-interacting electronic system. Experimental measurement of the correlation entropy is greatly challenging as it requires knowledge of all correlators in the whole system[25–27] . Machine learning methodologies algorithm offer a potential alternative strategy for extracting the correlation entropy from a reduced set of measurements [28] . Machine learning methods have been demonstrated to be highly successful in extracting  \n(a) Jk0 Jkn  \n Correlation entropy density   \nSpin Spin  \n(b)  \n.  \nNon-  \n.  \n.  \ninteracting electron  \nInput Hidden Output  \n.  \n. Particle-particle correlators Cij  \n. Density-density correlators fij  \nFIG. 1. (a) Schematic of the model. Two interacting spinson the two sides of the non-interacting chain induces manybody correlation via Kondo coupling. (b) Schematic of the workflow of the neural-network model, taking as input spatially resolved local correlators,","cbCairFiPgnAftY0","https://ap.wps.com/l/cbCairFiPgnAftY0","pdf",1899216,1,"English","en",105,"# Introduction\n# Model\n## Correlation entropy density\n# Machine-learning methodology\n## Transferability and noise robustness\n# Conclusions","[{\"question\":\"Why is the Kondo screening cloud difficult to characterize experimentally?\",\"answer\":\"Although experiments have confirmed the Kondo screening cloud, the detailed structure of the quantum many-body correlations is still elusive. Extracting correlation and entanglement properties typically requires knowledge of many correlators across the system.\"},{\"question\":\"What does the proposed machine-learning algorithm output?\",\"answer\":\"It uses spatially resolved local correlators as input and predicts the spatial profile of the correlation entropy density in real space, including overlap effects in a double-Kondo system.\"},{\"question\":\"How does the method reduce experimental requirements compared with conventional approaches?\",\"answer\":\"It bypasses the typical need to measure long-range non-local correlators by reconstructing local entanglement information from a reduced set of experimentally accessible local measurements.\"}]","Machine learning the Kondo entanglement cloud from local measurements | PDF",1785680648,20,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"machine-learning-the-kondo-entanglement-cloud-from-local-measurements","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/machine-learning-the-kondo-entanglement-cloud-from-local-measurements/117987/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":22,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-05","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is the Kondo screening cloud difficult to characterize experimentally?","Question",{"text":75,"@type":76},"Although experiments have confirmed the Kondo screening cloud, the detailed structure of the quantum many-body correlations is still elusive. Extracting correlation and entanglement properties typically requires knowledge of many correlators across the system.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the proposed machine-learning algorithm output?",{"text":80,"@type":76},"It uses spatially resolved local correlators as input and predicts the spatial profile of the correlation entropy density in real space, including overlap effects in a double-Kondo system.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the method reduce experimental requirements compared with conventional approaches?",{"text":84,"@type":76},"It bypasses the typical need to measure long-range non-local correlators by reconstructing local entanglement information from a reduced set of experimentally accessible local measurements.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":23},{"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":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":28,"slug":126},9,"Religion & Spirituality","religion-spirituality",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":28,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]