Machine learning for self-bound quantum systems

Abstract

In this work we compute the ground-state properties of one-dimensional systems composed of fully-polarized fermions interacting through an attractive Gaussian potential. If the interactions are able to overcome kinetic energy contributions, these particles can become bound without the presence of an external potential. We use Neural Quantum States, a technique which exploits deep neural networks as the ansatz for a Variational Monte Carlo. We adapt a previously presented network architecture, that was designed to enforce fermionic antisymmetry, to also include a mean-centering transformation. This fixes the system at the origin of space, overcoming numerical instabilities. Transfer learning from ansätze trained on systems trapped with an external potential is used to facilitate reaching a global energy minimum. We predict analytically and confirm computationally that, under certain conditions, these systems are fully characterized by their scattering length, giving rise to what we call “1D fermionic halo systems”. Our results suggest that the ground state energy decreases linearly with the amount of fermions and has an inverse quadratic dependence on the scattering length