We show that neural quantum states based on very deep (4–16-layered) neural networks can outperform state-of-the-art variational approaches on highly frustrated quantum magnets, including quantum-spin-liquid candidates. We focus on group convolutional neural networks that allow us to efficiently impose space-group symmetries on our ansätze. We achieve state-of-the-art ground-state energies for the $J_1-J_2$ Heisenberg models on the square and triangular lattices, in both ordered and spin-liquid phases, and discuss ways to access low-lying excited states in nontrivial symmetry sectors. We also compute spin and dimer correlation functions for the quantum paramagnetic phase on the triangular lattice, which do not indicate either conventional or valence-bond ordering.

• Received 24 May 2023
• Accepted 18 July 2023

DOI:https://doi.org/10.1103/PhysRevB.108.054410