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The basics of quantum Monte Carlo

Lucas K. Wagner, Jeffrey C. Grossman, Jeffrey B. Neaton

Published Jun 15, 2007• 0 citations
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arXiv:1307.4009•Physical Review B•Jul 25, 2013•11 citations
The quantum Monte Carlo (QMC) method is a modern many-body computational methodology which proves very successful for the studies of systems with pronounced electron correlation effects. We describe basic procedures necessary to achieve chemical accuracy (1 kcal/mol) in the estimation of energy differences. In order to extend the capabilities of our QMC procedure, we recently initiated a new development aimed at the evaluation of interatomic forces in molecular systems within the QMC framework. Here we present our current progress and preliminary results.
Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of ``best available'' values for the Fermi liquid parameters.