Learning by Confusion: The Phase Diagram of the Holstein Model

TL;DR

This paper introduces an unsupervised machine learning method using neural networks to detect phase transitions in the Holstein model, successfully constructing its finite-temperature phase diagram.

Contribution

It applies the 'learning by confusion' technique with convolutional neural networks to analyze quantum Monte Carlo data for the Holstein model, identifying phase transitions without prior labels.

Findings

Successfully identified critical points in the Holstein model

Constructed the finite-temperature phase diagram

Evaluated effectiveness of different training datasets

Abstract

We employ the "learning by confusion" technique, an unsupervised machine learning approach for detecting phase transitions, to analyze 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. Our results culminate in the construction of the finite-temperature phase diagram of the Holstein model.