Identifying phase transitions of disordered topological systems by unsupervised learning

Abstract
Phase transitions are critical in understanding the properties of different phases of matter, and their identification is an essential research focus in condensed matter physics. However, defining phase transitions for topological systems is more complex than for common mesoscale materials. This complexity is further compounded when disorders are present in the system.

In this thesis work, we provide a comprehensive review of machine learning, topological insulators, and the conventional approach to classifying different topological phases. We focus on the Benalcazar, Bernevig, and Hughes (BBH) model, a higher-order topological insulator model, and investigate the challenges of identifying phase transitions in topological systems, particularly in the presence of disorders.

To overcome these challenges, we implement the diffusion maps method, which accurately predicts the same transition points as traditional numerical calculations for both clean and disordered systems. Moreover, we demonstrate the efficacy of the diffusion maps method in predicting the transition point for the topological Anderson insulator. Our findings suggest that this approach has the potential to be generalized and applied to a broader range of disordered systems.

Overall, this thesis work provides a novel method for identifying phase transition points in topological systems, which could have significant implications for the design and development of future topological materials.

Citation
Sun, Y. (2023). Identifying phase transitions of disordered topological systems by unsupervised learning [KAUST Research Repository]. https://doi.org/10.25781/KAUST-52Y65

DOI
10.25781/KAUST-52Y65

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