Scaling and renormalization in the modern theory of polarization: application to disordered systems

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buir.contributor.authorHetényi, Balázs
buir.contributor.authorParlak, Selçuk
buir.contributor.authorYahyavi, Mohammad
buir.contributor.orcidHetényi, Balázs|0000-0002-3680-1147
buir.contributor.orcidParlak, Selçuk|0000-0001-6905-4814
buir.contributor.orcidYahyavi, Mohammad|0000-0003-0062-203X
dc.citation.epage214207-7en_US
dc.citation.issueNumber214207en_US
dc.citation.spage214207-1en_US
dc.citation.volumeNumber104en_US
dc.contributor.authorHetényi, Balázs
dc.contributor.authorParlak, Selçuk
dc.contributor.authorYahyavi, Mohammad
dc.date.accessioned2022-02-14T13:40:56Z
dc.date.available2022-02-14T13:40:56Z
dc.date.issued2021-12-15
dc.departmentDepartment of Physicsen_US
dc.description.abstractWe develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy in the scaling theory and in place of the Boltzmann probability in a position-space renormalization scheme. We derive a scaling relation between critical exponents which we test in a variety of models in one and two dimensions. We then apply the renormalization to disordered systems. In one dimension, the renormalized disorder strength tends to infinity, indicating the entire absence of extended states. Zero (infinite) disorder is a repulsive (attractive) fixed point. In two and three dimensions, at small system sizes, two additional fixed points appear, both at finite disorder: Wa(Wr) is attractive (repulsive) such that Wa<Wr. In three dimensions, Wa tends to zero and Wr remains finite, indicating a metal-insulator transition at finite disorder. In two dimensions, we are limited by system size, but we find that both Wa and Wr decrease significantly as system size is increased.en_US
dc.description.provenanceSubmitted by Burcu Böke (tburcu@bilkent.edu.tr) on 2022-02-14T13:40:56Z No. of bitstreams: 1 Scaling_and_renormalization_in_the_modern_theory_of_polarization_Application_to_disordered_systems.pdf: 1096446 bytes, checksum: 1fdfae35b5b1dbe9318666f9f1ba65b3 (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-14T13:40:56Z (GMT). No. of bitstreams: 1 Scaling_and_renormalization_in_the_modern_theory_of_polarization_Application_to_disordered_systems.pdf: 1096446 bytes, checksum: 1fdfae35b5b1dbe9318666f9f1ba65b3 (MD5) Previous issue date: 2021-12-15en
dc.identifier.doi10.1103/PhysRevB.104.214207en_US
dc.identifier.eissn2469-9969
dc.identifier.issn2469-9950
dc.identifier.urihttp://hdl.handle.net/11693/77336
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttps://doi.org/10.1103/PhysRevB.104.214207en_US
dc.source.titlePhysical Review Ben_US
dc.subjectCritical phenomenaen_US
dc.subjectElectric polarizationen_US
dc.subjectGeometric & topological phasesen_US
dc.subjectQuantum phase transitionsen_US
dc.subjectLattice models in condensed matteren_US
dc.subjectRenormalization groupen_US
dc.titleScaling and renormalization in the modern theory of polarization: application to disordered systemsen_US
dc.typeArticleen_US

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