Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics

C. J. Umrigar (Cornell Theory Center; Cornell University; Ithaca; Kingston; Laboratory of Atomic; M. P. Nightingale (Department of Physics; NY); RI); Solid State Physics; University of Rhode Island

arxiv: cond-mat/9804288 · v2 · pith:75CFR4D7new · submitted 1998-04-27 · ❄️ cond-mat

Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics

M. P. Nightingale (Department of Physics , University of Rhode Island , Kingston , RI) , C. J. Umrigar (Cornell Theory Center , Laboratory of Atomic , Solid State Physics , Cornell University

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keywords mechanicscarlomethodsmonteeigenvaluequantumstatisticalused

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In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.

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Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics

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