Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane

Abstract

Lattice field theories with a complex action can be studied numerically by allowing a complexified configuration space to be explored. Here we compare the recently introduced formulation on a Lefschetz thimble with the result from stochastic quantisation (or complex Langevin dynamics) in the case of a simple model and contrast the distributions being sampled. We also study the role of the residual phase on the Lefschetz thimble.

13 pages, 7 figures

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Cited by in corpus (42)

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• An efficient method to compute the residual phase on a Lefschetz thimble
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
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• Thimble regularization at work: from toy models to chiral random matrix theories
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• Complex saddle points and the sign problem in complex Langevin simulation
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• Path integral contour deformations for observables in $SU(N)$ gauge theory
• Path integral contour deformations for noisy observables
• An improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• The Dirac spectrum in Complex Langevin Simulations of QCD
• New developments for dual methods in lattice field theory at non-zero density
• Towards learning optimized kernels for complex Langevin
• Phase Unwrapping and One-Dimensional Sign Problems
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• 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
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• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Developments in lattice QCD for matter at high temperature and density
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• Quantum field theories on the Lefschetz thimble
• Lefschetz Thimble Quantum Monte Carlo for Spin Systems
• Localised distributions in complex Langevin dynamics
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• The Lefschetz thimble and the sign problem
• Extending complex Langevin simulations to full QCD at nonzero density
• Real-time quantum dynamics, path integrals and the method of thimbles
• Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density
• The Role of Integration Cycles in Complex Langevin Simulations
• Stable Evaluation of Lefschetz Thimble Intersection Numbers: Towards Real-Time Path Integrals
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• Combining complex Langevin dynamics with score-based and energy-based diffusion models