Accuracy of Restricted Boltzmann Machine wavefunctions for frustrated spin systems

Artificial neural networks (ANNs) constitute a powerful tool to approximate multi-variable functions in a plethora of different contexts. In the quest for an efficient representation of the ground state wavefunction of many-body quantum systems, ANNs have recently emerged as a flexible framework to construct variational ansatze [1]. We investigate the accuracy of Restricted Boltzmann Machine (RBM) networks as many-body Jastrow factors for the study of spin systems. In particular, we apply the RBM factor on top of a Gutzwiller-projected fermionic wavefunction [2], in order to construct a variational ansatz for the ground state of the spin-1/2 J₁-J₂ Heisenberg model in two dimensions. In the magnetically ordered phase (J₂=0), Monte Carlo results show that the RBM correlator yields a significant improvement of the variational energy [2]. On the other hand, when competing interactions are turned on and the system becomes highly frustrated, the energy gain due to the RBM becomes remarkably less pronounced.

[1] G. Carleo and M. Troyer, Science 355, 602 (2017).
[2] Y. Nomura, A. Darmawan, Y. Yamaji, and M. Imada, Phys. Rev. B 96, 205152 (2017).