Notice the unusual day and time!
BİLKENT UNIVERSITY DEPARTMENT of PHYSICS SEMINAR
“Number theory meets physics: the curious case of the Aubry-André model”
Abstract: The Aubry-André model captures the essence of quasiperiodicity. It consists of a hopping term between lattice sites and an on-site modulation which depends on an irrational parameter. In numerical calculations this parameter is taken to be the golden ratio and is approximated as a rational number through the ratio of consecutive Fibonacci numbers. In this talk I will present results of calculations for a many-body non-interacting Aubry-André system with periodic boundary conditions. We will use the geometric Binder cumulant and other localization sensitive quantities of the modern polarization theory to study the localization transition. We find that the phase diagram is not a simple function, it can not even be drawn. It is similar to a Dirichlet indicator function. At particle densities which extrapolate in the thermodynamic limit to a particular type of irrational number (one rationally well approximated by a ratio of Fibonacci numbers or sums thereof) we find that the system is always localized, otherwise a transition occurs at the potential strength at which single particle states are known to localize. Light is shed on this state of affairs by the use of the Zeckendorf theorem, which states that all natural numbers can be decomposed (almost) uniquely into a sum of Fibonacci numbers. The formation of „bands” in such a system, as distinct from systems for which the Bloch theorem is valid, will also be discussed. The phenomenon is robust: we show that similar behavior is found in an extended Aubry-André model.
References:
B. Hetényi and I. Balogh, Phys. Rev. B 112 144203 (2025).
B. Hetényi, Phys. Rev. B 110 125124 (2024).
Date: November 20, 2025 Thursday
Time: 13:30
Place: SA-240
All interested are cordially invited.