Extending earlier studies based mainly on configurations or auxiliary-field variables, we apply principal component analysis (PCA), an unsupervised dimensionality-reduction machine-learning method, to dynamical functions of quantum many-body systems obtained from numerically exact continuous-time quantum Monte Carlo simulations. We examine whether PCA can detect phase transitions and crossovers and reveal the underlying dynamical changes in the Hubbard, transverse-field Sherrington-Kirkpatrick (SK) spin glass, and Kondo models. In the Hubbard model, PCA is applied to spectral functions. We find that the leading principal-component (PC1) scores, which measure the projection onto the dominant variation, show an anomaly near the metal-insulator transition. The corresponding loading vector, which gives the weight of each frequency point in the dominant variation, identifies spectral weight transfer from the quasiparticle region around $\omega \approx 0$ to the Hubbard bands. Imaginary-time susceptibility data are used as PCA inputs for both the SK spin glass model and the Kondo model. In the spin glass model, PC1 scores develop a distinct feature at the glass transition as a function of the transverse field for several parameter sets, whereas in the Kondo model they follow universal scaling controlled by the Kondo temperature.

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• Glass transition
• Kondo effect
• Metal-insulator transition
• Phase transitions
• Quantum many-body systems
• Strongly correlated systems
• Dimensionality reduction
• Dynamical mean field theory
• Machine learning
• Quantum Monte Carlo