Switching Boundary Conditions in the Many-Body Diffusion Algorithm

TL;DR

This paper extends the many-body diffusion algorithm by incorporating boundary condition switching via permutation transpositions, enabling sign-problem-free simulations of complex quantum systems with variable potentials.

Contribution

It introduces a novel method to handle boundary condition switching in diffusion processes, avoiding potential invariance constraints and broadening applicability.

Findings

Successfully models boundary condition transitions using Markov chains.

Demonstrates feasibility with examples like harmonic fermions and ortho-helium.

Provides a sign-problem-free implementation scheme for complex systems.

Abstract

In this paper we show how the transposition, the basic operation of the permutation group, can be taken into account in a diffusion process of identical particles. Whereas in an earlier approach the method was applied to systems in which the potential is invariant under interchanging the Cartesian components of the particle coordinates, this condition on the potential is avoided here. In general, the potential introduces a switching of the boundary conditions of the walkers. These transitions modelled by a continuous-time Markov chain generate sample paths for the propagator as a Feynman-Kac functional. A few examples, including harmonic fermions with an anharmonic interaction, and the ground-state energy of ortho-helium are studied to elucidate the theoretical discussion and to illustrate the feasibility of a sign-problem-free implementation scheme for the recently developed many-body diffusion approach.