Quantum Criticality from Quantum Geometry

Low-dimensional topological insulators, a classic example of which are quantum Hall systems, can be tuned to a critical point with a subset of states becoming delocalized. Such extended states exhibit unusual self-similar multi-peak structure contributing to transport properties in a highly non-trivial way. Motivated by this problem, we investigate transport in the Su-Schrieffer-Heeger chain with chiral disorder, which hosts such critical states. We show that low-frequency conductivity in this system exhibits an unusual activated form, indicating a logarithmically slow tunneling regime of electronic propagation. Notably, this result emerges solely from the spatial profile of the impurity states. Therefore, in contrast to conventional diffusive metals, the structure of the wavefunctions plays a pivotal role in shaping the transport properties of topological critical systems.