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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Theoretical Aspects of Condensed Matter II

MP 9.1: Talk

Wednesday, March 20, 2024, 09:30–09:50, HL 102

Wegner model on a tree graph: U(1) symmetry breaking — •Julian Arenz — Institut für theoretische Physik, Zülpicher Str. 77, 50937 Köln

The Anderson transition between localized and metallic states is traditionally analyzed by assuming a one-parameter scaling hypothesis. However, there exists mounting evidence that the transition in d≥ 3 dimensions may have a second branch and that two relevant parameters are needed in order to describe the universal behavior at criticality. Doubt of the standard hypothesis also comes from field theory. Indeed, increasing the space dimension moves the Anderson transition point in the strong disorder regime. Here, a strong coupling approach very different from the usual weak-coupling analysis of the σ-model is called for.

In the process of developing the field theory at strong coupling we first investigate the N=1 Wegner model on a Bethe lattice assuming the self-consistent theory of localization due to Abou-Chacra et al. We derive a self consistency equation for the Fourier Laplace transform of a local matrix Green’s function. Its degree of freedom is a matrix field whose target is a space foliated by hyperboloids.

Our main observation is that the U(1) symmetry which distinguishes retarded from advanced fields may undergo spontaneous symmetry breaking. Put in other words, in the high dimension and large disorder regime there exist stable solutions that break U(1) symmetry.

Keywords: Anderson transitions at strong coupling; Disordered electron systems; U(1) symmetry breaking