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

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