Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model

Abstract

We study the finite size scaling of the bulk polarization in a quasiperiodic (Aubry-André) 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-André 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.

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• From generating functions to the geometric Binder cumulant
• Rashba Spin-Orbit Coupling and Nonlocal Correlations in Disordered 2D Systems
• Exact mobility edges in a slowly varying quasiperiodic ladder model
• Average density of Bloch electrons in a homogeneous magnetic field: A second-order response
• Disorder averaging in random lattice models with periodic boundary conditions: Application to models with uncorrelated and correlated disorder
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux