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Description

The “learning by confusion” technique is an unsupervised machine learning approach that can be used to detect physical phase transitions. We train our model with outputs of quantum Monte Carlo simulations of the two-dimensional Holstein model—a fundamental model for electron-phonon interactions on a lattice. Utilizing a convolutional neural network, we conduct a series of binary classification tasks to identify Holstein critical points based on the neural network’s learning accuracy. We further evaluate the effectiveness of various training datasets, including snapshots of phonon fields and other measurements resolved in imaginary time, for predicting distinct phase transitions and crossovers. We are then able to construct a machine-learned finite-temperature phase diagram of the Holstein model, showcasing new phase transition points that were previously impossible to obtain.