Reweighting Lefschetz Thimbles

Abstract

One of the main challenges in simulations on Lefschetz thimbles is the computation of the relative weights of contributing thimbles. In this paper we propose a solution to that problem by means of computing those weights using a reweighting procedure. Besides we present recipes for finding parametrizations of thimbles and anti-thimbles for a given theory. Moreover, we study some approaches to combine the Lefschetz thimble method with the Complex Langevin evolution. Our numerical investigations are carried out by using toy models among which we consider a one-site z^4 model as well as a U(1) one-link model.

arXiv comment11 pages, 9 figures, 2 tables; in revised version added a few references

References in corpus (22)

• The QCD phase diagram for small densities from imaginary chemical potential
• The QCD thermal phase transition in the presence of a small chemical potential
• Finite density QCD via imaginary chemical potential
• A new method to study lattice QCD at finite temperature and chemical potential
• High density QCD on a Lefschetz thimble?
• Simulating full QCD at nonzero density using the complex Langevin equation
• Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freeze-out in Heavy Ion Collisions
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Stochastic quantization at finite chemical potential
• A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
• Monte Carlo study of real time dynamics
• Structure of Lefschetz thimbles in simple fermionic systems
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Toward solving the sign problem with path optimization method
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• An efficient method to compute the residual phase on a Lefschetz thimble
• Stability of complex Langevin dynamics in effective models
• The density of states approach to dense quantum systems
• Application of neural network to sign problem via path optimization method
• One-dimensional QCD in thimble regularization
• Combining the complex Langevin method and the generalized Lefschetz-thimble method
• Gradient flows without blow-up for Lefschetz thimbles

Cited by in corpus (14)

• Review on novel methods for lattice gauge theories
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• Taylor expansions on Lefschetz thimbles (and not only that)
• Spinfoams and high performance computing
• Simulating Yang-Mills theories with a complex coupling
• Settling an old story: solution of the Thirring model in thimble regularization
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Towards sampling complex actions
• The small-$N$ series in the zero-dimensional $O(N)$ model: constructive expansions and transseries
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Correctness criteria for complex Langevin