Hidden-nucleons neural-network quantum states for the nuclear many-body problem

Understand

We generalize the hidden-fermion family of neural network quantum states to encompass both continuous and discrete degrees of freedom and solve the nuclear many-body Schr\"odinger equation in a systematically improvable fashion.

• We demonstrate that adding hidden nucleons to the original Hilbert space considerably augments the expressivity of the neural-network architecture compared to the Slater-Jastrow ansatz.
• The benefits of explicitly encoding in the wave function point symmetries such as parity and time-reversal are also discussed.
• Leveraging on improved optimization methods and sampling techniques, the hidden-nucleon ansatz achieves an accuracy comparable to the numerically-exact hyperspherical harmonic method in light nuclei and to the auxiliary field diffusion Monte Carlo in $^{16}$O.