Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes

TL;DR

This paper introduces advanced coordinate-space solvers HFB-AX and MADNESS-HFB for accurately modeling superfluid Fermi systems in large, complex spatial domains, enabling detailed studies of nuclear and atomic phenomena.

Contribution

It presents the development and benchmarking of two novel 3D and 2D coordinate-space solvers for the Hartree-Fock-Bogoliubov equations, improving computational efficiency and accuracy.

Findings

HFB-AX uses B-spline techniques with hybrid MPI/OpenMP parallelization.

MADNESS-HFB employs multi-resolution analysis for adaptive 3D calculations.

Benchmark results demonstrate the solvers' effectiveness on ultracold fermion systems.

Abstract

The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi systems with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.