Comparison of the numerical matrix multiplication and quantum Monte Carlo simulations: calculation of spatial delocalization parameters Original Research Article

An algebraic (= deterministic) scheme - the numerical matrix multiplication (NMM) - is used for the calculation of spatial expectation values and associated dispersions of a one-dimensional model system. The capability of the procedure is tested by computing the spatial atomic delocalization of a harmonic oscillator in thermodynamic equilibrium. The numerical data are compared with analytical results. The deterministic method yields highly accurate values even at very low temperatures. To obtain results of comparable accuracy with statistical quantum Monte Carlo (QMC) simulations a much higher computational effort is required, i.e. such simulations need a large number of QMC steps and time slices.