Machine Learning Phases of Strongly Correlated Fermions

TL;DR

This paper demonstrates how neural network machine learning techniques can classify phases of strongly correlated fermions in the Hubbard model, accurately predicting magnetic phase diagrams and transition trends with doping.

Contribution

It introduces a transfer learning approach using 3D convolutional neural networks trained on quantum Monte Carlo data to analyze phase transitions in correlated fermion systems.

Findings

Neural networks correctly predict the magnetic phase diagram at half filling.

Transfer learning extends the magnetic instability prediction to 5% doping.

The approach offers a new tool for studying quantum many-body systems.

Abstract

Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling). We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling. This transfer learning approach predicts that the instability to the magnetic phase extends to at least 5% doping in this region. Our results pave the way for other machine learning applications in correlated quantum many-body systems.