A comparison of energy estimators used in quantum Monte Carlo calculations

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The Journal of Chemical Physics, ISSN: 0021-9606, Vol: 83, Issue: 2, Page: 768-771

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https://digitalcommons.uri.edu/chm_facpubs/38; https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1037&context=chm_facpubs
J. D. Doll; David L. Freeman
AIP Publishing; DigitalCommons@URI
Physics and Astronomy; Chemistry
article description
Path-integral Monte Carlo calculations in quantum statistical mechanics have been performed using either discretized methods or Fourier methods. In each of these methods the internal energy has been calculated using either temperature differentiation or direct operation on the density matrix by the Hamiltonian. It is shown that the variance of the internal energy calculated by operation of the Hamiltonian on the density matrix in the Fourier method is independent of the number of Fourier components included in the expansion of the paths for a number of systems. The variance of the internal energy obtained from the other methods is shown to grow with the size of the expansion used for all systems. © 1985 American Institute of Physics.