Sign problem in finite density lattice QCD

TL;DR

This paper investigates a new sign problem in the canonical approach to finite density lattice QCD, where phase fluctuations of certain terms limit the method's effectiveness, especially at large densities.

Contribution

The study identifies a new sign problem related to phase fluctuations in the canonical approach and discusses potential solutions to mitigate this issue.

Findings

Complex phase of $z_n$ is proportional to $n$ at each Monte Carlo step.

Phase fluctuations become severe for large $n$, especially in the confinement phase.

These fluctuations impose a limit on the accessible range of $n$ in simulations.

Abstract

The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In the canonical approach, the grand partition function is written as a fugacity expansion: $Z_G(\mu,T) = \sum_n Z_C(n,T) \xi^n$, where $\xi=\exp(\mu/T)$ is the fugacity, and $Z_C(n,T)$ are given as averages over a Monte Carlo update, $\langle z_n\rangle$. We show that the complex phase of $z_n$ is proportional to $n$ at each Monte Carlo step. Although $\langle z_n\rangle$ take real positive values, the values of $z_n$ fluctuate rapidly when $n$ is large, especially in the confinement phase, which gives a limit on $n$. We discuss possible remedies for this problem.