Simulation of strongly quantum-degenerate uniform electron gas using the pseudo-fermion method

TL;DR

This paper demonstrates that the pseudo-fermion method effectively overcomes the fermion sign problem, enabling accurate simulations of strongly quantum-degenerate uniform electron gases where traditional methods fail.

Contribution

The study applies the pseudo-fermion method to strongly quantum-degenerate electron gases, showing it can accurately compute energies without the sign problem, surpassing existing techniques.

Findings

Pseudo-fermion method achieves 0.6% deviation from exact results.

It accurately simulates regimes where CPIMC and RPIMC fail.

The method enables sign-problem-free study of strongly quantum-degenerate systems.

Abstract

For strongly quantum-degenerate systems at finite temperatures, the fermion sign problem remains the major obstacle to first-principles simulations. In this work, we apply the recently proposed pseudo-fermion method - designed to overcome the sign problem - to strongly quantum-degenerate uniform electron gases. We find that the pseudo-fermion method can efficiently and highly accurately infer the energy of the uniform electron gas while being free from the fermion sign problem. For example, in the strongly quantum-degenerate regime where RPIMC fails (33 spin-polarized electrons at the density parameter $r_s = 0.5$), the relative deviation between the pseudo-fermion method and the exact CPIMC result is only 0.6%. In particular, the pseudo-fermion method bridges the gap where neither CPIMC nor RPIMC can accurately simulate the regime $1 \le r_s \le 2$ at the reduced temperature $\theta = 0.0625$. This work demonstrates that the pseudo-fermion method opens a new pathway for studying strongly quantum-degenerate systems in a sign-problem-free manner.