Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model

Understand

The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass.

• In order to understand its property, we consider the sign problem of the one-site fermion model appearing in its path-integral expression by using the Lefschetz-thimble method.
• We show that the original integration cycle becomes decomposed into multiple Lefschetz thimbles at a certain value of the fermion chemical potential, which would correspond to half of the pion mass of finite-density QCD.
• This triggers a fictitious phase transition on each Lefschetz thimble, and the interference of complex phases among them plays an important role for the correct description of the system.