Sample generation for the spin-fermion model using neural networks

Monte Carlo simulations of hybrid quantum-classical models such as the double exchange Hamiltonian require calculating the density of states of the quantum degrees of freedom at every step. Unfortunately, the computational complexity of exact diagonalization grows as a function of the system's size N, making it prohibitively expensive for any realistic system. We consider leveraging data-driven methods, namely, neural networks, to replace the exact diagonalization step in order to speed up sample generation. We explore a model that learns the free energy for each spin configuration and a second one that learns the Hamiltonian's eigenvalues. We implement data augmentation by taking advantage of the Hamiltonian's symmetries to artificially enlarge our training set and benchmark the different models by evaluating several thermodynamic quantities. While all models considered here perform exceedingly well in the one-dimensional case, only the neural network that outputs the eigenvalues is able to capture the right behavior in two dimensions. The simplicity of the architecture we use in conjunction with the model agnostic form of the neural networks can enable fast sample generation without the need of a researcher's intervention.

Automated summary

This article explores the use of neural networks to replace exact diagonalization in Monte Carlo simulations of hybrid quantum-classical models. By learning the free energy and the eigenvalues of the Hamiltonian, fast sample generation can be achieved. While all models perform well in one dimension, only the neural network outputting eigenvalues captures the correct behavior in two dimensions.