Learning the Holstein Model Quantum Phase Transitions by Confusion

We employ the "Learning by Confusion" technique, an unsupervised machine learning (ML) approach for detecting phase transitions, to analyze Quantum Monte Carlo (QMC) simulations of the two-dimensional Holstein model—a fundamental model for electron-phonon interactions. Utilizing a convolutional neural network (CNN) architecture, we conduct a series of binary classification tasks to identify Holstein critical points based on the ML model's accuracy. We further evaluate the effectiveness of various training datasets, including snapshots of Hubbard-Stratonovich fields and other measurements resolved in imaginary time, for predicting distinct phase transitions. Our results culminate in the construction of the finite-temperature phase diagram of the Holstein model.