Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model

Nilanjan Roy; Auditya Sharma

doi:10.1103/physrevb.103.075124

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arXiv · 2008.10561

Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model

Nilanjan Roy·Auditya Sharma

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Abstract

We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-André-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^σ}$) 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 $σ<1$ ($σ>1$). 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.

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cond-mat.dis-nn cond-mat.mes-hall cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el

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Nilanjan Roy, Auditya Sharma. 2021-02-13. Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model. https://doi.org/10.1103/physrevb.103.075124

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