CASINO manual - Theory of Condensed Matter

the DMC energy with a sufficiently low error bar. This is the ‘statistics-accumulation’ part 8 .
As usual, the basic output of casino is sent to a file called out. The other important output file
is dmc.hist, which contains the energy and other data as a function of move number (see Sec. 7.10
for precise definitions of what it contains). The data in this file must be analysed using the reblock
utility, as was done above for the data in the vmc.hist file—there is no equivalent of the ve utility
at present. Again, as in VMC, on-the-fly reblocking is done to a limited extent and reblocked error
bars are printed at the end of the output file (this will not work yet for continued runs; in that case
the reblock utility must be used) 9 .
The progress of a DMC simulation is easily visualized by means of the utility graphdmc, which reads
the dmc.hist file and calls the plotting program xmgrace to show you the resulting pretty picture.
Typing graphdmc will produce something like this:
1500
1400
1300
1200
1100
POPULATION
1000
0 500 1000 1500
-55.4
-55.5
-55.6
Local energy (Ha)
Reference energy
Best estimate
-55.7
-55.8
0 500 1000 1500
Number of moves
This picture shows the results of the simulation of an antiferromagnetic NiO crystal with 1280 configurations.
The upper panel shows how the population fluctuates as the simulation progresses. There
is a feedback process in operation to limit the population fluctuations, so the population should just
oscillate around the total initial number of configurations that we chose (1280 in this case). If you
have a colour-printed manual or you are looking at the PDF version, in the bottom panel you will see
a red line, a green line and a rapidly oscillating black line. The black line is the instantaneous value
of the local energy averaged over the current population of configurations; the red line is the reference
energy E T , which is adjusted to control the feedback process that keeps the population in check; and
the green line is the best estimate of the DMC energy as the simulation progresses.
You should note that, in the picture above, the best estimate of the energy falls from its initial value
(the energy from the VMC configuration-generation run) to a much lower, constant value (around
−55.72 a.u.) as the wave function evolves to the ground state. You should look for the point at which
8 Given our ability to reblock the casino data and discard an arbitrary number of initial steps, one might wonder
why it is necessary at all to run equilibration steps in DMC. In fact, the algorithm in the equilibration and statistics
accumulation phases is slightly different. In the equilibration phase, the underlying mean DMC energy is generally
expected to decrease as time progresses, whereas in the statistics accumulation phase it is steady. Hence the ‘best
estimate of the energy’ in equilibration is taken over a narrow window of the most recent ebest av window (=25 by
default) moves, whereas in statistics accumulation the best estimate is the average over all moves since the start of
statistics accumulation. The best estimate of the energy is used in the local-energy limiting schemes when computing
the branching factors: see later.
9 A file dmc.status is written and overwritten at the end of each DMC block. At any time during the run, this
file contains the complete statistical evaluation as it would be written if the run had finished here. The out file only
contains this data once at the end, if the run is finished properly. The file is intended to be both human-readable and
easy to parse.
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