Another type of error comes from the bias due to the trial wave
function. For the quantities measured as pure estimators no effect
was found. Also in the case of other estimators, such as the OBDM,
the use of an optimized trial wavefunction yields reasonably small
differences between mixed and variational estimators (less than
). In this case we believe that the extrapolated technique
of section 3.3.4 gives reliable results.
There is another source of error which arises from the hard-sphere
model. In the DMC method the particles propagate according to
diffusion (3.27) and drift (3.28) moves. Due to finite
timestep it can happen during the simulation that some particle
overlap with an impurity or another particle. This walker should
not contribute to the calculation of averages because it does not
satisfy the boundary conditions of the problem. One possibility is
to artificially eliminate the walker or to redo the last diffusion
jump so that it will choose another trajectory. Both of the choices
bring in a systematic error. It is hard to investigate the effect
of this error because it comes always mixed up with the timestep
errors (3.4.2) and it is impossible to separate two
effects. It is clear however that the percentage of the restarted
or removed walkers must be kept small. For example in our
calculations this percentage was always smaller than few percent.
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