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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• Lefschetz-thimble analysis of the sign problem in one-site fermion model
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• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Thimble regularization at work: from toy models to chiral random matrix theories
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
• One-dimensional QCD in thimble regularization
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Understanding of QCD at high density from Z3-symmetric QCD-like theory
• Quark number holonomy and confinement-deconfinement transition
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• Complex spectrum of finite-density lattice QCD with static quarks at strong coupling
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• Persistent homology analysis for dense QCD effective model with heavy quarks
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• Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW