The many-body diffusion algorithm, harmonic fermions

TL;DR

This paper introduces a sign-problem-free numerical scheme for simulating many-body quantum systems of identical particles in harmonic potentials, utilizing boundary conditions based on permutation symmetry to accurately sample antisymmetric states.

Contribution

It presents a novel implementation of the many-body diffusion approach that effectively handles antisymmetry and crossing effects without the sign problem.

Findings

The method successfully samples antisymmetric states.

Boundary conditions based on permutation symmetry are effective.

Crossing/recrossing effects are crucial for accuracy.

Abstract

A numerical implementation scheme is presented for the recently developed many-body diffusion approach for identical particles, in the case of harmonic potentials. The procedure is free of the sign problem, by the introduction of the appropriate absorption or reflection conditions for the walkers at the boundary of a state space. These conditions are imposed by the permutation symmetry. The outflow of the walkers at the boundary of the state space contributes substantially to the energy. Furthermore, the implementation of crossing/recrossing effects at absorbing boundaries proves indispensable to sample the antisymmetric states by discrete time steps.