Sample generation for the spin-fermion model using neural networks .*

We present a sample generation method for condensed matter systems based on machine learning. In our research, we used feedforward neural networks in conjunction with the Metropolis-Hastings algorithm to generate samples for the spin-fermion model. We compared two different neural networks and a linear model, based on the RKKY approximation, and found the neural networks outperforming the linear model. Given enough training data all models generated samples close to the true distribution. Furthermore, we present a way to leverage the neural networks and linear model trained on smaller systems to generate samples for significantly larger systems. Even though the samples generated have higher variance compared with samples generated using exact diagonalization of the full system, our results indicate that the generated samples can appropriately determine the average energy and specific heat of the full system. Lastly, we are going to discuss how the symmetries of the model can be exploited to reduce the number of data needed to train the neural networks.