[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127518-en":3,"doc-seo-127518-105":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},127518,13056712833777,"Logic","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states - Paper","We compute ground-state properties of fully polarized, trapped, one-dimensional fermionic systems with Gaussian pair interactions. An antisymmetric neural-network variational Ansatz, the neural quantum state, represents the wave function and minimizes the energy for systems of two to six particles. Extensive benchmarks compare the method against exact diagonalization and Hartree-Fock. The neural quantum state yields best energies over wide interaction strengths, capturing distinct phases controlled by the interaction sign: crystalline order for repulsion and bosonization signatures for strong attraction.","Machine learning one-dimensional spinless trapped fermionic systems with neural-network  \nquantum states  \nJ. W. T. Keeble  , 1 , * M. Drissi  , 1, 2 ,† A. Rojo-Francàs  ,3, 4 B. Juliá-Díaz  ,3, 4 and A. Rios 1, 3, 4  \n1 Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom  \n2 TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada  \n3 Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franquès 1, 08028, Barcelona, Spain  \n4 Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franquès 1, 08028, Barcelona, Spain  \n (Received 12 April 2023; revised 6 November 2023; accepted 20 November 2023; published 29 December 2023)  \nWe compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a Gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an Ansatz for the wave function and use machine learning techniques to variationally minimize the energy of systems from two to six particles. We provide extensive benchmarks for this toy model with other many-body methods, including exact diagonalization and the Hartree-Fock approximation. The neural quantum state provides the best energies across a wide range of interaction strengths. We find very different ground states depending on the sign of the interaction. In the nonperturbative repulsive regime, the system asymptotically reaches crystalline order. In contrast, the strongly attractive regime shows signs of bosonization. The neural quantum state continuously learns these different phases with an almost constant number of parameters and avery modest increase in computational time with the number of particles.  \nDOI: 10.1103/PhysRevA.108.063320  \nI. INTRODUCTION  \nThe emergence of machine learning (ML) within science has revolutionized numerous fields, from ab initio quantum chemistry to cosmology, by directly “learning” from data to understand physical phenomena [1] . Learning algorithms based on neural networks are underpinned by universal approximation theorems (UATs), which allow for, in principle, an arbitrary accuracy of data representation. UATs are, however, existence theorems, which state that such benefits are possible, but do not necessarily indicate how such benefits are achieved [2–5] . This allows for a wide range of research to build ML-based algorithms that represent physical phenomena, most notably the quantum many-body problem.  \nThe first use of ML in a quantum many-body system was pioneered in Ref. [6] and focused on discrete systems. Since then, several different physical systems have been tackled with these techniques [7–14] . Applications in quantum chemistry, like FermiNet [15, 16] or PauliNet [17, 18], have paved the way for accurate solutions of the electronic Schrödinger equation [19–23] . The marriage of quantum states and neural networks has led to the novel field of neural-network quantum states (NQSs) [9] .  \nML-based NQS approaches solve the Schrödinger equation variationally by representing the wave function as a  \n*[j.keeble@surrey.ac.uk](j.keeble@surrey.ac.uk)[ ](j.keeble@surrey.ac.uk)†[mdrissi@triumf.ca](mdrissi@triumf.ca)  \nPublished by the American Physical Society under the terms of the Creative Commons Attribution 4 .0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.  \nneural network [6] . NQSs are formulated so that they explicitly respect the symmetry of the many-body wave function, e.g., antisymmetry in the case of fermions. So far, there are indications that NQSs can compress the relevant information of many-body wave functions in a compact way [6,8, 15– 17,24–26] . While NQSs come in many different setups, firstquantized, real-space formulations are often employed to perform integrals over many-particle variables, using Monte Carlo (MC) tech","cbCaikI9zqjRJnFr","https://ap.wps.com/l/cbCaikI9zqjRJnFr","pdf",13414608,1,25,"English","en",105,"# Introduction\n## Motivation from machine learning in physics\n## Neural-network quantum states and variational formulation\n## Scope: one-dimensional spinless fermions in a harmonic trap\n## Fermi-Bose duality and interaction structure","[{\"question\":\"What system and interactions are studied in this work?\",\"answer\":\"The paper studies fully polarized (spinless) fermions in a one-dimensional harmonic trap with pairwise interactions characterized by a Gaussian potential.\"},{\"question\":\"How does the neural quantum state approach solve the problem?\",\"answer\":\"It uses an antisymmetric neural-network Ansatz for the fermionic wave function and variationally minimizes the energy to obtain ground-state properties.\"},{\"question\":\"What phases are identified as the interaction sign changes?\",\"answer\":\"In the repulsive nonperturbative regime the system asymptotically develops crystalline order, while in the strongly attractive regime the ground state shows signs consistent with bosonization.\"}]","Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states - Paper | PDF",1785939694,63,{"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-one-dimensional-spinless-trapped-fermionic-systems-with-neural-network-quantum-states-paper","",{"@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-one-dimensional-spinless-trapped-fermionic-systems-with-neural-network-quantum-states-paper/127518/",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 system and interactions are studied in this work?","Question",{"text":75,"@type":76},"The paper studies fully polarized (spinless) fermions in a one-dimensional harmonic trap with pairwise interactions characterized by a Gaussian potential.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the neural quantum state approach solve the problem?",{"text":80,"@type":76},"It uses an antisymmetric neural-network Ansatz for the fermionic wave function and variationally minimizes the energy to obtain ground-state properties.",{"name":82,"@type":73,"acceptedAnswer":83},"What phases are identified as the interaction sign changes?",{"text":84,"@type":76},"In the repulsive nonperturbative regime the system asymptotically develops crystalline order, while in the strongly attractive regime the ground state shows signs consistent with bosonization.","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},[93,97,101,105,110,115,120,123,128,131,135],{"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":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]