Erlangen 2026 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Quantum Mechanics: Spectral Theory and Many-Body Systems

MP 5.2: Vortrag

Mittwoch, 18. März 2026, 14:15–14:30, KH 02.013

Wegner model in high dimension: Singular continuous spectrum from AAT self-consistency and U(1) symmetry-breaking — •Julian Arenz — Institut für Theoretische Physik, Universität zu Köln

Adopting the self-consistent theory of localization due to Abou-Chacra, Anderson, Thouless (AAT), we analyze the N=1 Wegner model in high lattice dimension. By examining in detail the non-compact symmetry-breaking mechanism underlying the field theory, we uncover a new class of solutions of the AAT self-consistency equation. Their pattern of symmetry-breaking differs from the metallic and insulating solutions and naturally leads to a singular continuous spectrum of the Wegner Hamiltonian.

Keywords: Anderson transitions in high dimension; Singular continuous spectrum; Non-compact symmetry-breaking; Wegner model; Supersymmetric field theory in condensed matter