One-dimensional QCD in thimble regularization

Abstract

QCD in 0+1 dimensions is numerically solved via thimble regularization. In the context of this toy model, a general formalism is presented for SU(N) theories. The sign problem that the theory displays is a genuine one, stemming from a (quark) chemical potential. Three stationary points are present in the original (real) domain of integration, so that contributions from all the thimbles associated to them are to be taken into account: we show how semiclassical computations can provide hints on the regions of parameter space where this is absolutely crucial. Known analytical results for the chiral condensate and the Polyakov loop are correctly reproduced: this is in particular trivial at high values of the number of flavors N_f. In this regime we notice that the single thimble dominance scenario takes place (the dominant thimble is the one associated to the identity). At low values of N_f computations can be more difficult. It is important to stress that this is not at all a consequence of the original sign problem (not even via the residual phase). The latter is always under control, while accidental, delicate cancelations of contributions coming from different thimbles can be in place in (restricted) regions of the parameter space.

20 pages, 5 figures (many more pdf files) (one reference added)

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Cited by in corpus (22)

• Review on novel methods for lattice gauge theories
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Path integral contour deformations for observables in $SU(N)$ gauge theory
• A new dual representation for staggered lattice QCD
• Path optimization in 0+1 dimensional QCD at finite density
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Reweighting Lefschetz Thimbles
• Taylor expansions on Lefschetz thimbles (and not only that)
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Strong Coupling Lattice QCD in the Continuous Time Limit
• Dual Formulation and Phase Diagram of Lattice QCD in the Strong Coupling Regime
• Simulating Yang-Mills theories with a complex coupling
• Settling an old story: solution of the Thirring model in thimble regularization
• Lefschetz Thimble Quantum Monte Carlo for Spin Systems
• Instanton gas approach to the Hubbard model
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• Anatomy of a strong residual sign problem on the thimbles
• Sign optimization and complex saddle points in one-dimensional QCD
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models