QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing accuracy. Advances in real space methods include techniques for accurate computation of band gaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods including GW and density functional based techniques. To provide an improved foundation for these calculations we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK

Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond

In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the interpretation of ongoing and upcoming experiments in particle and nuclear physics, as well as inspire new ones.Comment: 44 pages. 1 of USQCD whitepapers

Approximating the Three-Nucleon Continuum

Three-nucleon forces (3NFs) are necessary to accurately describe the properties of atomic nuclei. These forces arise naturally together with two-nucleon forces (2NFs) when constructing nuclear interactions using chiral effective field theories (χEFTs) of quantum chromodynamics. Unlike phenomenological nuclear interaction models, χEFT promises a handle on the theoretical uncertainty in our description of the nuclear interaction. Recently, methods from Bayesian statistics have emerged to quantify this theoretical truncation error in physical predictions based on chiral interactions. Alongside quantifying the truncation error, the low-energy constants (LECs) of the chiral interactions must be inferred using selected experimental data. In this regard, the abundant sets of experimentally measured nucleon-nucleon (NN) and nucleon-deuteron (Nd) scattering cross sections serve as natural starting points to condition such inferences on. Unfortunately, the high computational cost incurred when solving the Faddeev equations for Nd scattering has thus far hampered Bayesian parameter estimation of LECs from such data. In this thesis, I present the results from a two-part systematic investigation of the wave-packet continuum discretisation (WPCD) method for reliably approximating two- and three-nucleon (NNN) scattering states with an aim towards a quantitative Bayesian analysis in the NNN continuum. In the first part, I explore the possibilities of using graphics processing units to utilise the inherent parallelism of the WPCD method, focusing on solving the Lippmann-Schwinger equation. In the second part, I use the WPCD method to solve the Faddeev equations for Nd scattering and analyse the reliability of the approximations of the WPCD method. This allows me to quantify the posterior predictive distributions for a range of low-energy neutron-deuteron cross sections conditioned on NN scattering data and NN interactions up to fourth order in χEFT

Nucleon-Nucleon Scattering in a Wave-Packet Formalism

In this thesis I analyse the prospect of leveraging statistical analyses of the strong nuclear interaction by using the wave-packet continuum discretisation (WPCD) method to efficiently compute nucleon-nucleon (NN) scattering observables on a graphics processing unit (GPU). The WPCD method gives approximate solutions to the S-matrix at multiple scattering energies at the cost of a single eigendecomposition of the NN channel Hamiltonian. In particular, I demonstrate and analyse the accuracy and inherent parallelism of the WPCD method by computing the most common NN scattering observables using a chiral Hamiltonian at next-to-next-to-leading order. I present an in-depth numerical study of the WPCD method and the GPU acceleration thereof. Additionally, I discuss which windows of opportunity are open for studying the strong nuclear interaction using data from few-nucleon scattering experiments