Sample generation for the spin-fermion model using neural networks

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.

8 pages, 5 figures

References in corpus (8)

• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields
• Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks
• The Truncated Polynomial Expansion Monte Carlo Method for Fermion Systems Coupled to Classical Fields: A Model Independent Implementation
• Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions
• Chebyshev expansion of spectral functions using restricted Boltzmann machines