2.6M - 1. Institut für Theoretische Physik - Universität Stuttgart

machines for an equal load. Because of branching the number of walkers varies. The
example output of the program is described and given in listing 4.3. The chapter ends
with some special hints as to the capacity of the used cluster of the HLRS (appendix E).
Comparison with other Methods: The results of the Variational and Diffusion Quantum
Monte Carlo simulation are compared by means of tables and diagrams. The ground
state energy E0 was determined for a constant external magnetic field, and decreases with
nuclear charge number Z . There is a correlation between tables and diagrams which are
arranged in order of the magnetic field strength B:
� B = 10 7 T: Table 5.1 (page 68), figures 5.1 up to 5.9 (page 71 up to 75)
� B = 5 · 10 7 T: Table 5.2 (page 68), figures 5.10 up to 5.22 (page 75 up to 81)
� B = 10 8 T: Table 5.3 (page 69), figures 5.23 up to 5.47 (page 82 up to 94)
� B = 5 · 10 8 T: Table 5.4 (page 70), figures 5.48 up to 5.72 (page 94 up to 106)
For clarity, the last column of each table contains the appropriate figure number. Both
tables and diagrams include values of other methods for a direct comparison:
� Hartree-Fock in adiabatic approximation with Finite Elements Method and Bspline
interpolation (HFFEM [14])
� 2 Dimensional Hartree-Fock (2DHF [8])
� Multi Configurational Perturbative Hybrid Hartree Hartree-Fock (MCPH 3 [21])
� Density Functional calculations (DF [11]).
The figures 5.1 up to 5.72 show the evolution of the trial energy ET, the block energy
EB and the average of the block energy 〈EB〉 plotted as a function of the number of the
block. The variable block is counted from 1 to 700 only for these figures, although each
part simulation starts internally with b = 1 and ends with b = bmax. The figures are
therefore partitioned in three areas marked by a vertical solid line. This line represents
the last block of the previous simulation. Each of these three areas is further separated
in two parts marked by a vertical dashed line dividing the part which does not count
to statistics (b = bs − 1) but is retained for achieving the dynamic equilibration. The
first 100 blocks refer to Variational Quantum Monte Carlo simulation (VQMC), the
blocks 101 up to 400 refer to fixed-phase Diffusion Quantum Monte Carlo simulation
(FPDQMC) and the blocks 401 up to 700 refer to released-phase Diffusion Quantum
Monte Carlo simulation (RPDQMC). Each block contains 200 steps. The HFFEM
calculations not only provide the ground state energy but also the adiabatic guiding
wavefunction Ψad G , which is afterwards multiplied by the Jastrow factor to obtain the
input guiding wavefunction of the DQMC simulation. The free parameter bJF of the
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