Introduction of Additive Particle Theory for Path Integral Approaches

TL;DR

This paper introduces Additive Particle (AP) theory, a novel approximation method for path integral approaches that avoids the sign problem in many-fermion systems by modeling electrons as string polymers with virtual particles.

Contribution

The paper presents AP theory, a new approximation that enables path integral analysis of fermion systems without the sign problem, and introduces star polymer variants.

Findings

AP theory can generate pair distribution functions for free electrons.

AP theory converges to free electron behavior at low electrostatic interactions.

Star polymer approximations extend the AP framework.

Abstract

Path integral approaches have been used for boson and fermion systems. The path integral approach has been successful in the many-boson system. However, in the many-fermion system, the path integral approach is not feasible due to the sign problem. In this letter, I introduce additive particle (AP) theory in order to generate an approximation method that avoids the sign problem. The AP theory considers one electron as a string polymer, and virtual particles are added into the system. The AP theory is an approximation, but it is constructed to be able to generate the pair distribution function between free electrons and the density of states of the free electrons at an arbitrary temperature. Hence, when the electrostatic interactions are decreased, the AP theory converges to the free electron system. On the other hand, it deviates from the actual system when the electrostatic interactions are increased. Star polymer approximation and extended star polymer approximation are also introduced.