Machine learning meets free parafermions: Revisiting the Z(N) model

We consider the non-Hermitian Z ( N ) free parafermion model from the perspective of machine learning. By neglecting the boundary contributions, key correlation functions obtained via the Hellmann–Feynman theorem are validated numerically. We implement unsupervised learning based on principal component analysis and k-means clustering to successfully detect and classify the phase transitions from the quasienergies. We also demonstrate the capability of fully connected neural networks in learning physical observables from the free parafermion formalism. Our results suggest an optimism towards finding an explicit exact formulation of the eigenvectors for N ≥ 3 .