The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry in which non-perturbative interactions are prominent. In the field of nuclear many-body theory, this complexity is exacerbated by the strong spin-isospin dependence of realistic nuclear interactions. As a consequence, the computational cost of evaluating standard Jastrow ansatz grows exponentially with the number of nucleons, limiting the applicability of quantum Monte Carlo methods to relatively small nuclear systems.
Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. Argonne researchers, in collaboration with Giuseppe Carleo of the Flatiron Institute, have introduced a neural-network quantum state ansatz to model the ground-state wave function of light nuclei and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, their approach has extended pioneering applications of ANNs in the field.
The researchers have computed the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a nuclear Hamiltonian derived within pionless effective field theory. To test this new method, they have successfully benchmarked the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions and virtually exact Green’s function Monte Carlo (GFMC) results. By leveraging advanced scientific software such as Tensorflow and Jax, the researchers will be able to easily deploy these ANN wavefunctions at scale onto current and future supercomputers, including Aurora.
Using computational resources provided by Argonne’s Joint Laboratory for System Evaluation, Laboratory Computing Resource Center, and Argonne Leadership Computing Facility, the researchers are now extending this method to include spin-isospin-dependent correlations and treat larger nuclear systems than currently possible.
Pictured above: ANN representation of the nuclear wave function. Curves show that ANN is equal to or outperforms traditional methods (GFMC) to solve for the ground state of 4He (right), accurately modeling nucleon densities even in the far tail (https://arxiv.org/abs/2007.14282, submitted to Physical Review Letters)