Dresden 2026 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 70: Correlated Electrons: Method Development III
TT 70.2: Vortrag
Donnerstag, 12. März 2026, 09:45–10:00, HSZ/0101
Real Green functions for the Anderson disorder model — •Marcus Kollar1, Martin Biehle1, Yannick Schäffer1, and Bas Lodewijks2 — 1Theoretical Physics III, Institute of Physics, University of Augsburg — 2Probability Group, School of Mathematical and Physical Sciences, University of Sheffield
Green functions for the Anderson model on the Bethe lattice fulfill a recursion relation, leading to a self-consistent solution for the complex self-energy [1]. Recently a new criterion for the localization transition was introduced [2] using the susceptibility of real cavity Green functions to changes of the disorder potential at distant lattice sites, which can be expressed in terms of repeated applications of an asymmetric integral kernel corresponding to the conditional probability distribution of cavity Green functions on neighboring sites. We derive a system of equations that connects this integral kernel and the distributions of real local and cavity Green functions to an arbitrary disorder distribution. For the special case of Cauchy disorder we use it to determine the Green function distributions explicitly for all energies. Furthermore for the band center we determine the complete kernel spectrum exactly, from which typical Lyapunov exponents and Green function correlation functions are obtained. Applications to other disorder distributions are also discussed.
[1] R. Abou-Chacra et al., J. Phys. C 6, 1734 (1973).
[2] G. Parisi et al., J. Phys. A 53, 014003 (2019).
Keywords: Anderson disorder model; Bethe lattice; cavity Green function; Cauchy probability distribution