[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125807-en":3,"doc-seo-125807-105":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},125807,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Machine learning reveals features of spinon Fermi surface","Rapid advances in simulating strongly interacting quantum Hamiltonians have made phase identification a key bottleneck. This work presents a quantum-classical hybrid approach (QuCl) that mines sampled projective snapshots using interpretable classical machine learning to expose signatures of states that look featureless. The method is tested on the Kitaev–Heisenberg model on a honeycomb lattice in an external magnetic field, where an intermediate gapless phase (IGP) is debated. A correlator CNN trained on labeled snapshots, combined with regularization path analysis, reproduces known phase signatures and identifies an IGP signature in the spin channel perpendicular to the field as Friedel oscillations of gapless spinons forming a Fermi surface. Predictions support future experimental searches for spin liquids.","arXiv :2306 .03143v2 [ cond-mat .str-el ] 11 Mar 2024  \nMachine learning reveals features of spinon Fermi surface  \nKevin Zhang, 1, ∗ Shi Feng,2 Yuri D. Lensky, 1, 3 Nandini Trivedi,2 and Eun-Ah Kim 1, 4, 5, 6  \n1 Department of Physics, Cornell University, Ithaca, NY, USA  \n2 Department of Physics, The Ohio State University, Columbus, OH, USA  \n3 Google Research, Mountain View, CA, USA  \n4 Radcliffe Institute for Advanced Studies, Cambridge, MA, USA  \n5 Department of Physics, Harvard University, Cambridge, MA, USA  \n6 Department of Physics, Ewha Womans University, Seoul, South Korea (Dated: March 12, 2024)  \nAbstract.  \nWith rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining sampled projective snapshots with interpretable classical machine learning can unveil signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice under external magnetic field presents an ideal system to test QuCl, where simulations have found an intermediate gapless phase (IGP) sandwiched between known phases, launching a debate over its elusive nature. We use the correlator convolutional neural network, trained on labeled projective snapshots, in conjunction with regularization path analysis to identify signatures of phases. We show that QuCl reproduces known features of established phases. Significantly, we also identify a signature of the IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for spin liquids.  \nIntroduction.  \nAs our ability to simulate quantum systems increases, there is a corresponding need for determining how to characterize unknown phases realized in simulators. Going from measurements to the nature of the underlying state is a challenging inverse problem. Full quantum state tomography [1] of the density matrix is impractical. Although the classical shadow [2] scales better than full tomography, the approach does not prescribe to researchers the proper observables to evaluate. Viewing the inverse problem as a data problem invites adopting machine learning methods: a quantum-classical hybrid approach. Machine learning has been widely applied for characterizing quantum states [3] . Such methods have been most fruitful with symmetry-broken states, with a diverse set of approaches increasingly bringing more interpretability and reducing bias [4–6] . The characteristic features of ordered phases are ultimately local and classical, hence ML models tuned for image processing have readily learned such features. By contrast, past learning of quantum states defined without order parameters has relied on theoretically guided feature preparation [7, 8] . However, such reliance on prior knowledge blocks the researchers’ access to new insights into unknown states: the ultimate goal of simulating quantum states.  \nTo push the limits of the nascent quantum-classical hybrid approach, we need a setting known to host anon-trivial quantum phase of unknown nature. Recent investigations into extended Kitaev models [9–12] have led to the observation of a mysterious intermediate gapless  \n∗ Corresponding author: [kz345@cornell.edu](kz345@cornell.edu)  \nphase (IGP) sandwiched between the Kitaev spin liquid and the trivial polarized state under a non-perturbative [111] magnetic field [13–16], whose identification presentsan interesting and important puzzle away from the perturbative limit. However, the nature of this field-induced IGP has raised debate in the community.  \nSeveral theories have shown evidence that supports a gapless quantum spin liquid phase with an emergent U(1) spinon Fermi surface [15, 17–19], while there are also mean field theories indicating tha","cbCaidUa1mAOb5Zn","https://ap.wps.com/l/cbCaidUa1mAOb5Zn","pdf",8528663,1,16,"English","en",105,"# Abstract\n# Introduction\n## Quantum-classical hybrid learning for phase identification\n## Intermediate gapless phase debate in Kitaev–Heisenberg\n# Quantum-Classical (QuCl) approach and benchmarking","[{\"question\":\"What is the Quantum-Classical hybrid approach (QuCl) used for in this study?\",\"answer\":\"QuCl mines sampled projective snapshots with interpretable classical machine learning to uncover signatures of quantum phases that may appear featureless. It supports phase identification as an inverse data problem.\"},{\"question\":\"Why is the Kitaev–Heisenberg model with an external magnetic field a suitable test case?\",\"answer\":\"It hosts a debated intermediate gapless phase (IGP) sandwiched between known phases, making it an ideal setting to test whether machine learning can reveal the IGP’s elusive nature.\"},{\"question\":\"What signature does QuCl identify for the intermediate gapless phase?\",\"answer\":\"It identifies a signature in the spin channel perpendicular to the field direction, interpreted as Friedel oscillations of gapless spinons forming a Fermi surface.\"}]","Machine learning reveals features of spinon Fermi surface | PDF",1785901321,40,{"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-reveals-features-of-spinon-fermi-surface","",{"@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-reveals-features-of-spinon-fermi-surface/125807/",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 Quantum-Classical hybrid approach (QuCl) used for in this study?","Question",{"text":75,"@type":76},"QuCl mines sampled projective snapshots with interpretable classical machine learning to uncover signatures of quantum phases that may appear featureless. It supports phase identification as an inverse data problem.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is the Kitaev–Heisenberg model with an external magnetic field a suitable test case?",{"text":80,"@type":76},"It hosts a debated intermediate gapless phase (IGP) sandwiched between known phases, making it an ideal setting to test whether machine learning can reveal the IGP’s elusive nature.",{"name":82,"@type":73,"acceptedAnswer":83},"What signature does QuCl identify for the intermediate gapless phase?",{"text":84,"@type":76},"It identifies a signature in the spin channel perpendicular to the field direction, interpreted as Friedel oscillations of gapless spinons forming a Fermi surface.","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},[93,97,101,105,110,115,119,122,127,130,134],{"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":29,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"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"]