Publication: Improving reptation quantum Monte Carlo

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Title Improving reptation quantum Monte Carlo
Authors/Editors* W.K. Yuen, D.G. Oblinsky, R.G. Giacometti, S.M. Rothstein
Where published* International Journal of Quantum Chemistry
How published* Journal
Year* 2009
Volume 109
Pages 3229-3242
Publisher Wiley
Keywords reptation quantum Monte Carlo, time-step bias, Metropolis-Hastings, Langevin diffusion
The reptation quantum Monte Carlo (RQMC) algorithm of Baroni and Moroni (Phys Rev Lett 1999; 82; 4745) is a recent and promising development. In this approach, one generates a large number of reptiles: sets of electron con gurations arising from consecutive drift-di usion moves. Within the xed-node approximation, one extracts estimates of the exact energy from reptiles' heads and tails (their rst and last con gurations of electrons, respectively), and estimates expectation values for operators that don't commute with the Hamiltonian, from their middle con gurations. An advantage over conceptually equivalent algorithms is that each estimate is free from population control bias. The time-step bias, however, may accumulate, adversely a ecting one's ability to accurately estimate physical properties of atoms and molecules. For this purpose we propose an alternative algorithm, 'head-tail adjusted' reptation quantum Monte Carlo, engineered to remedy this de ciency, while still simulating the target distribution for RQMC. The e ectiveness of our approach is demonstrated by an application to ground-state LiH. We estimate the fi xed-node energy with improved reliability, without adversely a ecting the quality of other, non-energy-related properties' estimates.
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