Bosonic Neural Quantum States in Continuous Space

Neural quantum states (NQS) have been shown to be a powerful tool in the computation of ground-states for several quantum mechanical many-body systems.

While the field has mainly focused on Hamiltonians defined on discrete lattices, there is an increasing interest in the properties of continuous systems.

Recently, results have been reported for non-periodic, continuous systems such as molecules.

In this work we will show that it is possible to use a permutation-invariant neural-network architecture to approximate the wavefunction of periodic, bosonic systems if care is taken to correctly enforce continuity at the boundaries.

The method is general and can in principle be applied to arbitrary Hamiltonians in an arbitrary number of spatial dimensions.

We will present the application of the architecture to two different interaction potentials (Helium-4 and Gaussian) in one and two spatial dimensions. We will outline the shortcomings of the current approach and ways to improve the obtained accuracy.