Quantum Critical Dynamics Induced by Topological Zero Modes

We investigate low-frequency ac transport in the Su-Schrieffer-Heeger (SSH) chain with chiral disorder near the topological delocalization transition. Our key finding is that the formation of hybridized pairs of topological domain wall zero modes leads to the anomalous logarithmic scaling of the ac conductivity σ(ω)∼logω at criticality, and σ(ω)∼ω^{2|δ|}log^{2}ω away from it. Using the combination of real-space renormalization group analysis and qualitative hybridization arguments, we demonstrate that the form of the scaling of ac conductivity at criticality stems directly from the stretched-exponential [ψ(x)∼e^{-ssqrt[x]}] spatial decay of zero-mode wave functions at the critical point.