Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model
Balázs Hetényi
Abstract
We study the finite size scaling of the bulk polarization in a quasiperiodic (Aubry-Andr\'e) model using the geometric analog of the Binder cumulant. As a proof of concept, we show that the geometric Binder cumulant method described here can reproduce the known literature values for the flat and raised cosine distributions, which are the two distributions that occur in the delocalized phase. For the Aubry-Andr\'e model at half-filling, the phase transition point is accurately reproduced. Not only is the correct size scaling exponent of the variance obtained in the extended and the localized phases, but the geometric Binder cumulant undergoes a sign change at the phase transition. We also calculate the state resolved Binder cumulant as a function of disorder strength to gain insight into the mechanism of the localization transition.