ELFT HÍRADÓ

[Kormos Márton <kormos.marton AT ttk.bme.hu>]

MEGHÍVÓ

BME Elméleti Fizika Szeminárium,

feb. 20. péntek 10h15,

1111 Budapest, Budafoki út 8., BME F III. magasföldszint 01.,
Elméleti Fizika Tanszék szemináriumi szoba

  Hetényi Balázs (BME Elm. Fiz. Tanszék, HUN-REN Wigner Fizikai Kutatóközpont)
  
  Number theory meets physics: the curious case of the Aubry-André model

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.  Turning on 
disorder broadens these features, offering hope that it is experimentally 
measurable. 


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).


Minden érdeklődőt szeretettel várunk.

Kormos Márton,
szemináriumi koordinátor