Sample generation for the spin-fermion model using neural networks

TL;DR

This paper explores neural network models to replace exact diagonalization in quantum Monte-Carlo simulations of the spin-fermion model, significantly speeding up sample generation especially in two-dimensional systems.

Contribution

It introduces neural network approaches to predict eigenvalues and free energy, leveraging symmetries for data augmentation, and demonstrates their effectiveness in two-dimensional quantum models.

Findings

Neural networks accurately predict thermodynamic quantities in 1D.

Only the eigenvalue-predicting neural network performs well in 2D.

Model simplicity enables fast, automated sample generation.

Abstract

Quantum 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 $ \mathcal{O} (N^3)$ 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.