Sample generation for the spin-fermion model using neural networks [article]

Georgios Stratis, Phillip Weinberg, Tales Imbiriba, Pau Closas, Adrian E. Feiguin
2022 arXiv   pre-print
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 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
more » ... 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.
arXiv:2206.07753v1 fatcat:7a5io2dgbvahvbr765hemsrhxu