Machine learning and the magnetic phases of correlated fermions

Machine learning has emerged as an exciting new tool to study phases and phase transitions of models in statistical mechanics and condensed matter physics in the past couple of years. In this talk, I will discuss the application of artificial neural network machine learning techniques to predict the finite-temperature magnetic phase diagram of strongly correlated lattice fermions. I will show results for the classification of auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model at commensurate filling, and discuss how the learning can be transferred to gain insight about the fate of the ordered phase as the system is doped. In the last part, I will present results from several unsupervised machine learning and dimension reduction algorithms and show that they capture the physics of the model as the temperature is varied in the weak-coupling region.
K. Ch'ng, J. Carrasquilla, R. G. Melko, E. Khatami, Phys. Rev. X 7, 031038 (2017)
K. Ch'ng, N. Vazquez, E. Khatami, arXiv:1708.03350