Scaling of the Integrated Quantum Metric in Disordered Topological Phases

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.

6 pages, 3 figures

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• Quantum response theory and momentum-space gravity
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
• Evaluation of real-space second Chern number using the kernel polynomial method
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Regularized universal topological markers for Dirac systems
• Quantum geometry, localization, and topological bounds of spin fluctuations