Göttingen 2025 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Poster Session: Many-body Theory

MP 9.3: Poster

Mittwoch, 2. April 2025, 16:15–18:15, ZHG Foyer 1. OG

Wegner model in high dimension: Self-consistent approximation — •Julian Arenz — Cologne University, Zülpicher Straße 77, 50937 Köln

Assuming the self-consistent theory of localization due to Abou-Chacra, Anderson and Thouless (AAT), we study the N=1 Wegner model in the regime of strong disorder and high dimension.

While it is traditionally believed that the Wegner model possesses only two phases (metallic and insulating), we investigate the existence of a third phase with spontaneously broken U(1) symmetry. We do so by using a supersymmetric integral equation which follows from the AAT self-consistency equation for the advanced and retarded Green’s function.

In the process, we uncover solutions that are neither of metallic nor of insulating type (they break a U(1) symmetry but have a non-compact symmetry). We propose that these solutions correspond to the novel phase and describe fractal eigenstates and singular continuous spectrum.

Keywords: Anderson transitions in high dimension; Fractal eigenstates; Self consistent theory of localization; Supersymmetry