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- W3127586382 abstract "We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-Andr'e-Harper(AAH) model with power-law hoppings ($sim frac{1}{r^sigma}$) when the quasiperiodicity parameter is chosen to be a member of the `metallic mean family' of irrational Diophantine numbers. In addition to the fully delocalized and localized phases we find a co-existence of multifractal (localized) states with the delocalized states for $sigma<1$ ($sigma>1$). The fraction of delocalized eigenstates in these phases can be obtained from a general sequence, which is a manifestation of a mathematical property of the `metallic mean family'. The entanglement entropy of the noninteracting many-body ground states respects the area-law if the Fermi level belongs in the localized regime while logarithmically violating it if the Fermi-level belongs in the delocalized or multifractal regimes. The prefactor of logarithmically violating term shows interesting behavior in different phases. Entanglement entropy shows the area-law even in the delocalized regime for special filling fractions, which are related to the metallic means." @default.
- W3127586382 created "2021-02-15" @default.
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- W3127586382 date "2021-02-11" @default.
- W3127586382 modified "2023-10-03" @default.
- W3127586382 title "Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model" @default.
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- W3127586382 doi "https://doi.org/10.1103/physrevb.103.075124" @default.
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