Speaker
Description
One of the most frequently cited experimental results in condensed matter physics are those of the quantum Hall effect. These results show peaks in the Hall conductance as a function of magnetic flux at rational numbers of elementary flux units, implying that the experiment distinguishes between rational and irrational flux. In this talk I will present results for the Aubry-André model, a model which is equivalent to the Harper model (used to understand the quantum Hall effect). We study the model as a function of particle density and find that sharp peaks (spikes) occur in the localization-delocalization phase diagram: at rational fillings the transition occurs at a finite potential strength, while at certain accessible irrational fillings, the system is always localized (the transition occurs at zero potential strength). Our studies use extensions of the modern theory of polarization which casts the polarization as a geometric phase, rather than an operator expectation value. We have developed the analog of the Binder cumulant for geometric phases. To explain the presence of spikes, we invoke the Zeckendorf decomposition of natural numbers as an explanation. Time permitting we will connect our results to those of the quantum Hall effect.
B. Bánfalvi and B. Hetényi, work in progress.
B. Hetényi and I. Balogh, Phys. Rev. B 112 144203 (2025).
B. Hetényi, Phys. Rev. B 110 125124 (2024).