Sign problem in finite density lattice QCD

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, $⟨z_n⟩$. We show that the complex phase of $z_n$ is proportional to $n$ at each Monte Carlo step. Although $⟨z_n⟩$ 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.

Comments: 7 pages, 6 figures