Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution

Abstract

We consider a generalized Thirring model in 0+1 dimensions at finite density. In order to deal with the resulting sign problem we employ stochastic quantization, i.e., a complex Langevin evolution. We investigate the convergence properties of this approach and check in which parameter regions complex Langevin evolutions are applicable in this setting. To this end we derive numerous analytical results and compare directly with numerical results. In addition we employ indirect indicators to check for correctness. Finally we interpret and discuss our findings.

13 pages, 16 figures; v2: published version with changed title, corrected typos and added references

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• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• Parallel tempering algorithm for integration over Lefschetz thimbles
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Tempered transitions between thimbles
• Complex saddle points and the sign problem in complex Langevin simulation
• Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
• Complex Langevin simulations and the QCD phase diagram: Recent developments
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Stable solvers for real-time Complex Langevin
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Semidefinite Programs at Finite Fermion Density
• Deep Learning of Fermion Sign Fluctuations
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• Comparison between Fermion Bag Approach and Complex Langevin Dynamics for Massive Thirring Model at Finite Density in 0 + 1 Dimensions
• Correctness criteria for complex Langevin
• Path optimization method for the sign problem caused by fermion determinant