Variational Neural Network Quantum States for Frustrated Magnetic Systems

We investigate the Shastry-Sutherland model (SSM), i.e., spin-1/2 quantum Heisen- berg model on a Shastry-Sutherland lattice, using a newly emerging approach exploiting well-developed machine learning techniques. We utilize neural networks as variational quantum states in quantum Monte Carlo investigations of the ground state properties. We first focus on SSM without an external magnetic field. For small lattices accessible via exact diagonalization, we compare the precision of various architectures based on re- stricted Boltzmann machines (RBM) or group-convolutional neural networks. The most versatile and precise architecture, namely complex-valued RBM, is then applied for larger lattices. Here we investigate the frustrated regime. We show that the RBM is able to represent all three of the major and fundamentally different phases of SSM. Finally, we apply the complex-valued RBM for SSM in a finite external magnetic field. We find that it cannot capture the intriguing steps in magnetization typical for SSM correctly due to its tendency to prefer more ordered states with higher magnetization.