AG Mathematische Physik, Joris De Moor (FAU): Footprint of a topological phase transition on the density of states

Joris De Moor (FAU)

Footprint of a topological phase transition on the density of states

Abstract:
For a one-dimensional random discrete Schrödinger operator, the energies at
which all transfer matrices commute and have their spectrum off the unit circle
are called critical hyperbolic. Disorder driven topological phase transitions in
such models are characterized by a vanishing Lyapunov exponent at the critical
energy. It is shown that the density of states away from a transition has a
pseudogap with an explicitly computable Hölder exponent, while it has a
logarithmic divergence (Dyson spike) at the transition points. The proof is
based on renewal theory for the Prüfer phase dynamics and the optional stopping
theorem for martingales of suitably constructed comparison processes.