Peter Reynolds
Algorithms for Computing Matrix Elements by Quantum Monte Carlo
We describe a number of algorithms for computing expectation values of
quantities other than energies, in particular expectation values of
coordinate operators. In addition, the calculation of matrix elements
involving multiple states will be addressed, demonstrating for example
the evaluation of transition dipole moments, which are necessary for
the computation of oscillator strengths and lifetimes. The simple,
approximate, second-order or "extrapolated" estimator will be shown
for both expectation values and off-diagonal matrix elements, and
compared with the considerably more complex and computationally
demanding exact algorithms. The latter include one which employs a
single QMC random walk, and another which involves a VMC random walk
with auxiliary QMC ``side walks.'' A tagging algorithm used for
efficiently tracking descendants of a walker will be described for
each approach. For the single-walk algorithm it is found that
carrying weights together with branching significantly improves
efficiency. Exploitation of the correlation between VMC and QMC
expectation values is also considered. Large increases in efficiency
in the second approach are found when such correlations are
incorporated. Results will be presented for simple test systems. The
effect of Monte Carlo parameters such as time step size and
convergence time will be discussed.
NATO ASI, Cornell Theory Center,
Last modified: Fri Jul 3 10:04:57 EDT 1998