Efficient Calculation of Energy Spectra Using Path Integrals

TL;DR

This paper presents an improved path integral method that significantly accelerates the calculation of energy spectra in quantum systems, demonstrating efficiency gains through Monte Carlo simulations across various models.

Contribution

Introduces a hierarchy of effective actions that enhances the convergence and speed of path integral Monte Carlo calculations for energy spectra.

Findings

Achieves several orders of magnitude speedup in energy level computations.

Demonstrates effectiveness across multiple models.

Validates the method with explicit Monte Carlo simulations.

Abstract

A newly developed method for systematically improving the convergence of path integrals for transition amplitudes, introduced in Phys. Rev. Lett. 94 (2005) 180403, Phys. Rev. B 72 (2005) 064302, Phys. Lett. A 344 (2005) 84, and expectation values, introduced in 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.