Footprint of a topological phase transition on the density of states
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Date
2023
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Abstract
For a generalized Su–Schrieffer–Heeger model, the energy zero is always critical and hyperbolic in the sense that all reduced transfer matrices commute and have their spectrumofftheunitcircle.Disorder-driventopologicalphasetransitionsinthismodel are characterized by a vanishing Lyapunov exponent at the critical energy. It is shown that away from such a transition the density of states vanishes at zero energy with an explicitly computable Hölder exponent, while it has a characteristic 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.
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Keywords
Dyson spike, Topological phase transition, Hyperbolic critical energy