Variational and green's function Monte Carlo calculations of few-body systems

Francesco Pederiva, Alessandro Roggero, Kevin E. Schmidt

David M. Arnow, Malvin H. Kalos, Michael A. Lee +1 more

The Green’s function Monte Carlo method used for obtaining exact solutions to the Schrödinger equation of boson systems is generalized to treat systems of several fermions. We show that when it is possible to select eigenfunctions of the Hamiltonian based on physical symmetries, the GFMC method can be used to yield the lowest energy state of that symmetry. In particular, the lowest totally antisymmetric eigenfunction, the fermion ground state, can be obtained. Calculations on several two- and three-body model problems show the method to be computationally feasible for few-body systems.

Brian Pudliner

Recently, a realistic nucleon-nucleon potential has been developed with the goal of accurately reproducing isospin symmetry breaking effects in the nuclear interaction. We briefly discuss the motivation for this potential, called Argonne $v\sb{18},$ as well as the Urbana models of three-nucleon interactions. Our approach for modeling the ground states of nuclear systems begins with the development of a variational wave function. We discuss the basis for our variational wave functions and the Monte Carlo techniques used to evaluate expectation values with these wave functions. To determine the exact ground state, Green's function Monte Carlo (GFMC) techniques are used. We review the method of GFMC in general and then discuss its application to the problem of nuclear ground states in some detail.

Malvin H. Kalos

Pengsheng Wen, Alexandros Gezerlis, Jeremy W. Holt

Finding high-quality trial wave functions for quantum Monte Carlo calculations of light nuclei requires a strong intuition for modeling the interparticle correlations as well as large computational resources for exploring the space of variational parameters. Moreover, for systems with three-body interactions, the wave function should account for many-body effects beyond simple pairwise correlations. In this Letter, we design neural networks that efficiently incorporate these factors to generate expressive wave function Ansätze for light nuclei using variational Monte Carlo. Our neural-network approach for A=3 nuclei can capture, already at the level of variational Monte Carlo, the overwhelming majority of the ground-state energy estimated by Green's function Monte Carlo (GFMC). It achieves a ground-state energy within 0.45% of the GFMC result for ^{3}H using the softest chiral interaction, representing a substantial improvement over standard variational Monte Carlo, which exhibits a 3.7% deviation. The result indicates the potential of neural networks to construct effective trial wave functions for quantum Monte Carlo calculations.

Theoretical Physics