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

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.