CASINO manual - Theory of Condensed Matter

V(x)
Ψ init
(x)
τ{
t
Ψ 0
(x)
x
The first step in DMC is to generate these configurations in their initial distribution (i.e., according
to the VMC trial wave function). This is done through a VMC calculation in exactly the same way as
we generated configurations for variance minimization in the previous section. Therefore one should
again set vmc nconfig write to be the desired number of configurations, and vmc nstep to be ≥
vmc nconfig write. (Setting the decorrelation period vmc decorr period to a higher value than
in VMC is less important than in variance minimization, since the correlations will disappear as the
DMC calculation evolves).
Note—and this is a common point of confusion—that the runtype flag should generally be set to
‘vmc dmc’ at the start of a DMC calculation, not, as might be thought, to ‘dmc’ 7 .
An appropriate number of configurations to use for DMC might be 1000 or more. You can sometimes
get away with using a few hundred for small systems. Notice that parallelization is automatic—
configurations will be distributed among the nodes.
Following configuration generation the distribution of walkers is allowed to propagate in imaginary
time (see e.g. Ref. [11]) according to the DMC rules. During a certain period of equilibration, the
distribution will change until the walkers are distributed according to the ground-state wave function
of the system, subject to the constraint that the wave function has the same nodes as the trial function
that we started with. This part of the process is called ‘DMC equilibration’. The best estimate of
the energy will fall from the initial VMC value to around the correct ground-state energy during this
process. After equilibration, the best estimate of the energy will be roughly correct, and we now
propagate for a long period of imaginary time in order to accumulate enough energy data to estimate
7 Sometimes one does wish to do DMC only (by using already generated VMC configurations, or by continuing an
existing DMC run) in which case one should set runtype to either ‘dmc equil’ (perform DMC equilibration), ‘dmc stats’
(perform DMC statistics DMC equilibration), or ‘dmc dmc’ (perform DMC equilibration, then statistics accumulation).
In earlier versions of the code, we used runtype = ‘dmc’ with the now-deprecated keyword iaccumulate = T or F
to indicate whether stats accumulation was activated or not. This usage is now deprecated and, unless iaccumulate
is specifically defined in input, runtype = ‘dmc’ is just a synonym for ‘dmc dmc’. If you don’t know what DMC
equilibration or statistics accumulation are, read on.
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