Strictly localized states on the Socolar dodecagonal lattice

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buir.contributor.authorKeskiner, Mehmet Akif
buir.contributor.authorOktel, Mehmet Özgür
buir.contributor.orcidKeskiner, Mehmet Akif|0000-0003-3023-2761
buir.contributor.orcidOktel, Mehmet Özgür|0000-0001-8921-8388
dc.citation.epage064207-18en_US
dc.citation.issueNumber6en_US
dc.citation.spage064207-1en_US
dc.citation.volumeNumber106en_US
dc.contributor.authorKeskiner, Mehmet Akif
dc.contributor.authorOktel, Mehmet Özgür
dc.date.accessioned2023-02-15T08:30:15Z
dc.date.available2023-02-15T08:30:15Z
dc.date.issued2022-08-22
dc.departmentDepartment of Physicsen_US
dc.description.abstractSocolar dodecagonal lattice is a quasicrystal closely related to the better-known Ammann-Beenker and Penrose lattices. The cut and project method generates this twelvefold rotationally symmetric lattice from the six-dimensional simple cubic lattice. We consider the vertex tight-binding model on this lattice and use the acceptance domains of the vertices in perpendicular space to count the frequency of strictly localized states. We numerically find that these states span fNum 7.61% of the Hilbert space. We give 18 independent localized state types and calculate their frequencies. These localized state types provide a lower bound of fLS = 10919−6304√3 2 0.075854, accounting for more than 99% of the zero-energy manifold. Numerical evidence points to larger localized state types with smaller frequencies, similar to the Ammann-Beenker lattice. On the other hand, we find sites forbidden by local connectivity to host localized states. Forbidden sites do not exist for the Ammann-Beenker lattice but are common in the Penrose lattice. We find a lower bound of fForbid 0.038955 for the frequency of forbidden sites. Finally, all the localized state types we find can be chosen to have constant density and alternating signs over their support, another feature shared with the Ammann-Beenker lattice.en_US
dc.identifier.doi10.1103/PhysRevB.106.064207en_US
dc.identifier.eissn2469-9969
dc.identifier.issn2469-9950
dc.identifier.urihttp://hdl.handle.net/11693/111308
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttps://www.doi.org/10.1103/PhysRevB.106.064207en_US
dc.source.titlePhysical Review Ben_US
dc.titleStrictly localized states on the Socolar dodecagonal latticeen_US
dc.typeArticleen_US
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