Energy levels and expectation values via accelerated path integral Monte Carlo

A recently developed method systematically improved the convergence of generic path integrals for transition amplitudes, partition functions, expectation values and energy spectra. This was achieved by analytically constructing a hierarchy of discretized effective actions indexed by a level number p and converging to the continuum limit as 1/N^p. Here we apply the above general method to numerical calculations using Metropolis Monte Carlo simulations of energy expectation values and energy spectra. We analyze and compare the ensuing increase in efficiency of several orders of magnitude.