Revisiting the fermion sign problem from the structure of Lee-Yang zeros. I. The form of the partition function for anyons and its zeros at 0 K

Abstract

We connect the fermion sign problem (FSP) with the Lee-Yang theory of phase transitions, extend the symmetry parameter $\xi$ (bosons $\xi=1$, fermions $\xi=-1$) to the complex plane, and discover that the partition function of indistinguishable particles is a polynomial in $\xi$, so that all systems possess fixed zeros at zero temperature in the $\xi$ space that depend only on the particle number. This paper is Part I of a series revisiting the fermion sign problem from the structure of Lee-Yang zeros.

Together, the three papers of this series establish a theoretical framework for studying the FSP via Lee-Yang theory, explain the limitations of current path-integral-based fermionic methods, and guide the development of methods for solving the fermion sign problem.

Citation

He, Zeng, Yang, Wang, Ye, Li. 2026. “Revisiting the fermion sign problem from the structure of Lee-Yang zeros. I. The form of the partition function for anyons and its zeros at 0 K.” Physical Review E 113 (2): 024115.

@article{HZY26a,
author = {He and Zeng and Yang and Cong Wang and Ye and Li},
year = {2026},
title = {Revisiting the fermion sign problem from the structure of Lee-Yang zeros. I. The form of the partition function for anyons and its zeros at 0 K},
journal = {Physical Review E},
volume = {113},
number = {2},
pages = {024115}}