Coordinate-Space Solver for Superfluid Many-Fermion Systems with Shifted Conjugate Orthogonal Conjugate Gradient Method

TL;DR

This paper introduces a shifted conjugate-orthogonal conjugate-gradient method to efficiently compute densities in superfluid many-fermion systems, avoiding explicit quasiparticle wavefunction construction and reducing computational costs.

Contribution

The paper presents a novel shifted COCG approach for evaluating Green's functions in superfluid systems, improving efficiency and scalability over traditional diagonalization methods.

Findings

Successfully applied to nuclei with axial symmetry

Accurately modeled the $^{240}$Pu fission saddle point

Simulated neutron star crust vortex states

Abstract

Self-consistent approaches to superfluid many-fermion systems in 3-dimensions (and subsequent time-dependent approaches) require a large number of diagonalizations of very large dimension hermitian matrices, which results in enormous computational costs. We present an approach based on the shifted conjugate-orthogonal conjugate-gradient (COCG) method for the evaluation of the Green's function, from which we subsequently extract various densities (particle number, spin, current, kinetic energy, etc.) of a nuclear system needed in self-consistent approaches. The approach eschews the construction of the quasiparticle wavefunctions and their corresponding quasiparticle energies, which are never explicitly needed in any density functional approaches. As benchmarks we present calculations for nuclei with axial symmetry, including the ground state of spherical (magic or semi-magic) and axially deformed nuclei, the saddle-point in the $^{240}$Pu constrained fission path, and a vortex in the neutron star crust.