An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms

TL;DR

This paper derives an exact formula for fermion dynamics using Poisson processes, linking it to Monte Carlo algorithms, and introduces an optimal algorithm that aligns with Green Function Monte Carlo in the exact limit.

Contribution

It provides a novel derivation of fermion dynamics via a Feynman-Kac formula expressed through Poisson processes, connecting it to existing Monte Carlo methods.

Findings

Derived a Feynman-Kac type formula for fermions.

Established a family of algorithms based on Poisson processes.

Identified an optimal algorithm equivalent to Green Function Monte Carlo in the exact limit.

Abstract

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo method in the limit when the latter becomes exact.