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However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in d = 2 + ε of a U (N) Gross-Neveu model in the limit N → 0. Unfortunately, this model is not multiplicatively renormalizable in 2+ε dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one-loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a d = 4 − ε expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.","publication_date":"2015,,","publication_name":"Journal of Contemporary History","grobid_abstract_attachment_id":"90778525"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"The Journal of Contemporary History: Fifty Years of Change and Continuity","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [29619893]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card ds-work-card--prominent-pdf"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":90778525,"attachmentType":"pdf"}"><img alt="First page of “The Journal of Contemporary History: Fifty Years of Change and Continuity”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/90778525/mini_magick20220908-1-170k8f1.png?1662616642" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">The Journal of Contemporary History: Fifty Years of Change and Continuity</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="29619893" href="https://nationalww2museum.academia.edu/BradleyHart"><img alt="Profile image of Bradley W Hart" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/29619893/10115631/20120534/s65_bradley.hart.jpg" />Bradley W Hart</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2015, Journal of Contemporary History</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">13 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 86294244; 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However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in d = 2 + ε of a U (N) Gross-Neveu model in the limit N → 0. Unfortunately, this model is not multiplicatively renormalizable in 2+ε dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one-loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a d = 4 − ε expansion. 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Syzranov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annual Review of Condensed Matter Physics</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"High-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors, and Related Systems","attachmentId":77859024,"attachmentType":"pdf","work_url":"https://www.academia.edu/66809277/High_Dimensional_Disorder_Driven_Phenomena_in_Weyl_Semimetals_Semiconductors_and_Related_Systems","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/66809277/High_Dimensional_Disorder_Driven_Phenomena_in_Weyl_Semimetals_Semiconductors_and_Related_Systems"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="126059395" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/126059395/Short_Note_on_the_Density_of_States_in_3D_Weyl_Semimetals">Short Note on the Density of States in 3D Weyl Semimetals</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="164969719" href="https://independent.academia.edu/sinnerandreas">andreas sinner</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Short Note on the Density of States in 3D Weyl Semimetals","attachmentId":119994778,"attachmentType":"pdf","work_url":"https://www.academia.edu/126059395/Short_Note_on_the_Density_of_States_in_3D_Weyl_Semimetals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/126059395/Short_Note_on_the_Density_of_States_in_3D_Weyl_Semimetals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="7" data-entity-id="66809290" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/66809290/Unconventional_localisation_transition_in_high_dimensional_semiconductors_and_Weyl_semimetals">Unconventional localisation transition in high-dimensional semiconductors and Weyl semimetals</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="54255807" href="https://independent.academia.edu/SSyzranov">S. 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B 96, 155112, 2017</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fermion-induced quantum critical points in three-dimensional Weyl semimetals","attachmentId":57354926,"attachmentType":"pdf","work_url":"https://www.academia.edu/37391541/Fermion_induced_quantum_critical_points_in_three_dimensional_Weyl_semimetals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/37391541/Fermion_induced_quantum_critical_points_in_three_dimensional_Weyl_semimetals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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href="https://tsinghua.academia.edu/ShaoKaiJian">Shao-Kai Jian</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Phys. 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Lett. 114, 237001, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Emergent space-time supersymmetry in 3D Weyl semimetals and 2D Dirac semimetals","attachmentId":57354739,"attachmentType":"pdf","work_url":"https://www.academia.edu/37391387/Emergent_space_time_supersymmetry_in_3D_Weyl_semimetals_and_2D_Dirac_semimetals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/37391387/Emergent_space_time_supersymmetry_in_3D_Weyl_semimetals_and_2D_Dirac_semimetals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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