Publication: Improving reptation quantum Monte Carlo

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Title Improving reptation quantum Monte Carlo
Authors/Editors* W-K. Yuen, D. Oblinsky, R. D. Giacometti, S. M. Rothstein
Where published* International Journal of Quantum Chemistry
How published* Journal
Year* 2009
Volume 109
Pages 0000-0000
Publisher Wiley
Keywords quantum Monte Carlo, time-step bias
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 configurations arising from consecutive drift-diffusion moves. Within the fixed-node approximation, one extracts estimates of the exact energy from reptiles' heads and tails (their first and last configurations of electrons, respectively), and estimates expectation values for operators that do not commute with the Hamiltonian, from their middle configurations. An advantage over conceptually equivalent algorithms is that each estimate is free from population control bias. The time-step bias, however, may accumulate, adversely affecting 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 deficiency, while still simulating the target distribution for RQMC. The effectiveness of our approach is demonstrated by an application to ground-state LiH. We estimate the fixed-node energy with improved reliability, without adversely affecting the quality of other, nonenergy-related properties' estimates.
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