Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
| Autor: | Nilanjan Roy, Auditya Sharma |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Condensed Matter - Mesoscale and Nanoscale Physics Fermi level 02 engineering and technology Quantum entanglement Multifractal system Condensed Matter - Disordered Systems and Neural Networks 021001 nanoscience & nanotechnology Condensed Matter::Disordered Systems and Neural Networks 01 natural sciences Condensed Matter - Strongly Correlated Electrons symbols.namesake Delocalized electron Quasiperiodicity Entropy (classical thermodynamics) Quasiperiodic function Quantum mechanics 0103 physical sciences symbols Condensed Matter - Quantum Gases 010306 general physics 0210 nano-technology Condensed Matter - Statistical Mechanics Phase diagram |
| Zdroj: | Physical Review B. 103 |
| ISSN: | 2469-9969 2469-9950 |
| DOI: | 10.1103/physrevb.103.075124 |
| Popis: | 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 $\sigma1$). 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. Comment: 10 pages, 13 figures |
| Databáze: | OpenAIRE |
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