Scaling of the Integrated Quantum Metric in Disordered Topological Phases

TL;DR

This paper introduces a scalable numerical method to analyze how disorder affects quantum geometry in topological phases, revealing nontrivial behaviors in large disordered systems.

Contribution

It develops an efficient linear-scaling approach to study the quantum metric and Chern number in disordered topological systems at experimental scales.

Findings

Disorder influences the quantum metric and Chern number in topological phases.

The method enables analysis of large disordered systems with high computational efficiency.

Results show nontrivial behavior of topological invariants under disorder.

Abstract

We report a study of a disorder-dependent real-space representation of the 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 nontrivial behavior of the integrated quantum metric and Chern number in disordered systems with sizes reaching the experimental scale. We illustrate this approach in the disordered Haldane model, examining the impact of Anderson disorder and vacancies on the trivial and topological phases captured by this model.