A topological proof that there is no sign problem in one dimensional Path Integral Monte Carlo simulation of fermions

TL;DR

This paper demonstrates that in one-dimensional fermionic systems, the topology ensures positivity of the path integral, eliminating the sign problem in Monte Carlo simulations despite individual propagators being sign-changing.

Contribution

It provides a topological proof that the sign problem does not occur in 1D fermionic Path Integral Monte Carlo simulations.

Findings

Closed-loop propagator products are always positive in 1D due to topology.

Sign problem is absent in 1D fermionic PIMC simulations.

Topological properties guarantee positivity despite antisymmetric propagators.

Abstract

This work shows that, in one dimension, due to its topology, a closed-loop product of short-time propagators is always positive, despite the fact that each anti-symmetric free fermion propagator can be of either sign.