Wegner model on a tree graph: U(1) symmetry breaking and a non-standard phase of disordered electronic matter

TL;DR

This paper investigates the N=1 Wegner model on a tree graph under strong disorder, revealing a novel phase with broken U(1) symmetry linked to fractal eigenstates and singular spectra.

Contribution

It introduces a new non-standard electronic phase with U(1) symmetry breaking, providing a field-theory basis for complex spectral phenomena in disordered systems.

Findings

Discovery of a non-standard phase with U(1) symmetry breaking

Connection to fractal eigenstates and singular continuous spectra

Extension of self-consistent localization theory

Abstract

Assuming the self-consistent theory of localization due to Abou-Chacra et al., we solve the N=1 Wegner model in the regime of strong disorder and high dimension. In the process, we uncover a non-standard electronic phase with spontaneously broken U(1) symmetry -- the missing field-theory basis underlying phenomena associated with fractal eigenstates and singular continuous spectra.