Multi-electron systems in strong magnetic fields II: A fixed-phase diffusion quantum Monte Carlo application based on trial functions from a Hartree–Fock–Roothaan method

Abstract

We present a quantum Monte Carlo application for the computation of energy eigenvalues for atoms and ions in strong magnetic fields. The required guiding wave functions are obtained with the Hartree–Fock–Roothaan code described in the accompanying publication (Schimeczek and Wunner, 2014). Our method yields highly accurate results for the binding energies of symmetry subspace ground states and at the same time provides a means for quantifying the quality of the results obtained with the above-mentioned Hartree–Fock–Roothaan method. Program summaryProgram title: MantecaCatalogue identifier: AETV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 72284No. of bytes in distributed program, including test data, etc.: 604948Distribution format: tar.gzProgramming language: C++.Computer: Cluster of 1–∼500 HP Compaq dc5750.Operating system: Linux.Has the code been vectorized or parallelized?: Yes. Code includes MPI directives.RAM: 500 MB per nodeClassification: 2.1.External routines: Boost::Serialization, Boost::MPI, LAPACK BLASNature of problem:Quantitative modelings of features observed in the X-ray spectra of isolated neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product iron, at high magnetic field strengths. The predominant amount of line data in the literature has been calculated with Hartree–Fock methods, which are intrinsically restricted in precision. Our code is intended to provide a powerful tool for calculating very accurate energy values from, and thereby improving the quality of, existing Hartree–Fock results.Solution method:The Fixed-phase quantum Monte Carlo method is used in combination with guiding functions obtained in Hartree–Fock calculations. The guiding functions are created from single-electron orbitals ψi which are either products of a wave function in the z-direction (the direction of the magnetic field) and an expansion of the wave function perpendicular to the direction of the magnetic field in terms of Landau states, ψi(ρ,φ,z)=Pi(z)∑n=0NLtinϕni(ρ,φ), or a full two-dimensional expansion using separate z-wave functions for each Landau level, i.e. ψi(ρ,φ,z)=∑n=0NLPni(z)ϕni(ρ,φ). In the first form, the tin are expansion coefficients, and the expansion is cut off at some maximum Landau level quantum number NL. In the second form, the expansion coefficients are contained in the respective Pni.Restrictions:The method itself is very flexible and not restricted to a certain interval of magnetic field strengths. However, it is only variational for the lowest-lying state in each symmetry subspace and the accompanying Hartree–Fock method can only obtain guiding functions in the regime of strong magnetic fields.Unusual features:The program needs approximate wave functions computed with another method as input.Running time:1 min–several days. The example provided takes approximately 50 min to run on 1 processor.