Efficient calculation of energy spectra using path integrals

A newly developed method for systematically improving the convergence of path integrals for transition amplitudes [A. Bogojević, A. Balaž, A. Belić, Phys. Rev. Lett. 94 (2005) 180403, A. Bogojević, A. Balaž, A. Belić, Phys. Rev. B 72 (2005) 064302, A. Bogojević, A. Balaž, A. Belić, Phys. Lett. A 344 (2005) 84] and expectation values [J. Grujić, A. Bogojević, A. Balaž, Phys. Lett. A 360 (2006) 217] is here applied to the efficient calculation of energy spectra. We show how the derived hierarchies of effective actions lead to substantial speedup of the standard path integral Monte Carlo evaluation of energy levels. The general results and the ensuing increase in efficiency of several orders of magnitude are shown using explicit Monte Carlo simulations of several distinct models.