Peter Nightingale
Basics and quantum Monte Carlo-statistical mechanics overlap

  1. Generalized Metropolis algorithm; error bars.
  2. Evaluation of matrix elements of the form <u_a|G^p X G^q|u_b>/<u_a|G^(p+q)|u_b> for G_{ij} that can be written as G_{ij}=P_{ij} g_{ij}, where P is a Markov matrix and g_{ij} are non-negative weights.
    1. Evaluation by means of single-thread Monte Carlo averages, re-weighted by products of weights. (variational and "pure" diffusion Monte Carlo; projector Monte Carlo)
    2. Evaluation by application of the Metropolis algorithm directly to the distribution G_{ij}G_{jk} ...G_{mn} times "boundary effects" for i and n (path-integral Monte Carlo) Evaluation by means of branching Monte Carlo (diffusion Monte Carlo; transfer matrix Monte Carlo; forward walking)
  3. Trial function optimization emphasizing sub-dominant (excited) states (minimization of variance of local energy and generalizations).

Draft of lecture notes
More comprehensive paper

NATO ASI, Cornell Theory Center,

Last modified: Thu Jun 11 17:20:05 EDT 1998