Approximately symmetric neural quantum states for quantum spin liquids

Quantum spin liquids are exotic phases of strongly-correlated matter which exhibit an emergent gauge symmetry. However, for arbitrary Hamiltonians in a given spin liquid phase, the exact form of the symmetry operators is often not known. In order to exploit these symmetries, we propose an approximately group-invariant neural network as a variational ansatz for the ground state wavefunction. We split the network into two stages, one which enforces the gauge symmetries in a parameter regime in which they take a simple form, and the other to adiabatically transform the model to that regime. These tailored-made architectures are parameter-efficient and scalable. They significantly outperform existing neural network architectures without gauge symmetries, and are competitive with state-of-the-art quantum Monte Carlo and DMRG methods, as we demonstrate on a perturbed toric code model at large system sizes. This paves the way towards studying traditionally challenging quantum spin liquid problems within interpretable neural network architectures.