Stochastic perturbation theory: a prequel to Reptation Quantum Monte Carlo

Abstract

I present a different approach to Rayleigh-Schrödinger perturbation theory, based on Laplace transforms and polynomial theory, yielding an iterative expression for the perturbative expansion of the energy of the non-degenerate ground state of a quantum system, which easily lends itself to symbolic computation. A stochastic interpretation of the various perturbative corrections naturally leads to a re-summation scheme that is equivalent to Reptation Quantum Monte Carlo and that actually provided the original motivation to its development in the late nineties.

arXiv comment8 pages, no figures. Paper presented at CECAM workshop on "Recent developments in quantum Monte Carlo", Rome, October 21-22, 2021

References in corpus (2)

• The itinerant ferromagnetic phase of the Hubbard model
• Invariance principles in the theory and computation of transport coefficients