Quantum Critical Dynamics Induced by Topological Zero Modes

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.

11 pages, 4 figures

References in corpus (14)

• Anderson Transitions
• Observation of the topological Anderson insulator in disordered atomic wires
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Low-frequency conductivity in many-body localized systems
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Dynamics and transport in random quantum systems governed by strong-randomness fixed points
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Phases and phase transitions in disordered quantum systems
• Dynamical conductivity at the dirty superconductor-metal quantum phase transition
• Strong-disorder renormalization-group study of the one-dimensional tight-binding model
• Sinai Diffusion at Quasi-1D Topological Phase Transitions
• Anatomy of topological Anderson transitions
• Enhanced quantum metric due to vacancies in graphene
• On the Mott formula for the a.c. conductivity and binary correlators in the strong localization regime of disordered systems