Quantum Critical Dynamics Induced by Topological Zero Modes

TL;DR

This paper studies the ac transport properties of the SSH chain near the topological transition, revealing anomalous logarithmic scaling due to zero mode hybridization.

Contribution

It uncovers the critical scaling of ac conductivity caused by topological zero modes and their hybridization, using real-space renormalization group analysis.

Findings

Logarithmic scaling of ac conductivity at criticality

Hybridization of zero modes causes anomalous transport behavior

Spatial decay of zero modes explains the scaling form

Abstract

We investigate the 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 $\sigma(\omega) \sim \log \omega$ at criticality, and $\sigma(\omega) \sim \omega^{2 \delta} \log ^2 \omega$ 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 ($\psi(x) \sim e^{-s \sqrt{x}}~\,$) spatial decay of zero-mode wavefunctions at the critical point.