Scaling of the Quantum Geometry Metrics in Disordered Topological Phases

We report a study of disorder-dependent quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can explore the nontrivial behavior of the quantum geometry metrics (quantum metric and Chern number) in large-scale inhomogeneous systems, accounting for the presence of disorder. We illustrate this approach in the disordered Haldane model, examining the impact of Anderson and vacancy-type of disorders on the trivial and topological phases captured by this model.