Semi-supervised learning of topological phases in the disordered Haldane-Hubbard model

We examine the emergence of topological Anderson insulating phases in the spinful Haldane model with Hubbard and nearest-neighbor density-density interactions. Finite-size exact diagonalization is used to assess the different phases resulting from the interplay between topology, interactions and disorder. By combining unsupervised and supervised machine learning methods, in particular diffusion maps and convolutional neural networks, we predict the phase diagrams of the model as a function of disorder and interactions strengths, circumventing the explicit calculation of the Chern number and accurately predicting the multiple phases with finite disorder. Our method provides an efficient route to identify the C = 2 topological Anderson insulator phases present at zero and finite staggered mass. Remarkably, the diffusion map components can be interpreted as a transformation of the SDW and CDW structure factors. Finally, we report the effects of disorder on the antiferromagnetic C=1 phase, whose origin has been discussed extensively and lately reported to emerge at zero staggered mass as a disorder-induced state.