Landau levels in lattices with long - range hopping

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dc.citation.epage033612-10en_US
dc.citation.issueNumber3en_US
dc.citation.spage033612-1en_US
dc.citation.volumeNumber88en_US
dc.contributor.authorAtakişi, Hakanen_US
dc.contributor.authorOktel, M. Özgüren_US
dc.date.accessioned2016-02-08T09:35:39Z
dc.date.available2016-02-08T09:35:39Z
dc.date.issued2013en_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractLandau levels (LLs) are broadened in the presence of a periodic potential, forming a barrier for accurate simulation of the fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight-binding lattice if a particular form of long-range hopping is introduced. In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are infinitely many long-range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wave functions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restores the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wave functions is as large as the space spanned by continuum wave functions, and we find the constraints on the magnetic field for this condition to be satisfied. Finally, using these constraints and the first Chern numbers, we identify the bands of the Hofstadter butterfly that correspond to continuum LLs.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:35:39Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2013en_US
dc.identifier.doi10.1103/PhysRevA.88.033612en_US
dc.identifier.issn1050-2947
dc.identifier.urihttp://hdl.handle.net/11693/20810
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevA.88.033612en_US
dc.source.titlePhysical Review Aen_US
dc.subjectAnalytic expressionsen_US
dc.subjectChern numbersen_US
dc.subjectDiscretizationsen_US
dc.subjectFractional quantumen_US
dc.subjectGeneral methoden_US
dc.subjectHopping modelsen_US
dc.subjectLandau levelsen_US
dc.subjectPeriodic potentialsen_US
dc.subjectQuantum hall effecten_US
dc.subjectRestorationen_US
dc.subjectWave functionsen_US
dc.titleLandau levels in lattices with long - range hoppingen_US
dc.typeArticleen_US

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