English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the ground state conduction properties of noninteracting electronsin aperiodic but non-random one-dimensional models with chiral symmetry, andmake comparisons against Anderson models with non-deterministic disorder. Thefirst model we consider is the Fibonacci lattice, which is a paradigmatic modelof quasicrystals; the second is the Riemann lattice, which we define inspiredby Dyson's proposal on the possible connection between the Riemann hypothesisand a suitably defined quasicrystal. Our analysis is based on Kohn'smany-particle localization tensor defined within the modern theory of theinsulating state. In the Fibonacci quasicrystal, where all single-particleeigenstates are critical (i.e., intermediate between ergodic and localized),the noninteracting electron gas is found to be a conductor at most electrondensities, including the half-filled case; however, at various specificfillings $\rho$, including the values $\rho = 1/g^n$, where $g$ is the goldenratio and $n$ is any integer, the gas turns into an insulator due to spectralgaps. Metallic behaviour is found at half-filling in the Riemann lattice aswell; however, in contrast to the Fibonacci quasicrystal, the Riemann latticeis generically an insulator due to single-particle eigenstate localization,likely at all other fillings. Its behaviour turns out to be alike that of theoff-diagonal Anderson model, albeit with different system-size scaling of theband-centre anomalies. The advantages of analysing the Kohn's localizationtensor instead of other measures of localization familiar from the theory ofAnderson insulators (such as the participation ratio or the Lyapunov exponent)are highlighted.

Conduction in quasi-periodic and quasi-random lattices: Fibonacci, Riemann, and Anderson models