On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem

TL;DR

This paper introduces a method to interpolate between bosons and fermions using a real parameter, enabling the calculation of fermionic thermodynamic properties and potentially alleviating the fermion sign problem in quantum simulations.

Contribution

The authors develop a generalized path integral approach for fictitious particles with a continuous parameter, allowing thermodynamic properties of fermions to be obtained via extrapolation from bosonic-like systems.

Findings

The average energy as a function of the interpolation parameter is analytically well-behaved.

The method accurately computes fermionic energies at finite temperature.

It offers a new approach to mitigate the fermion sign problem in quantum Monte Carlo simulations.

Abstract

By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter $\xi$ interpolating continuously between bosons ($\xi=1$) and fermions ($\xi=-1$). Through general analysis and numerical experiments we find that the average energy may have good analytical property as a function of this real parameter $\xi$, which provides the chance to calculate the thermodynamical properties of identical fermions by an extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for $\xi\geq 0$. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion sign problem for some quantum systems.