Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral

Abstract

The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.

6 pages, 1 figure, typos corrected

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Cited by in corpus (7)

• Vacuum structure of bifundamental gauge theories at finite topological angles
• One-dimensional QCD in thimble regularization
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density
• Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model