Path optimization method for the sign problem caused by fermion determinant

Abstract

The path optimization method with machine learning is applied to the one-dimensional massive lattice Thirring model, which has the sign problem caused by the fermion determinant. This study aims to investigate how the path optimization method works for the sign problem. We show that the path optimization method successfully reduces statistical errors and reproduces the analytic results. We also examine an approximation of the Jacobian calculation in the learning process and show that it gives consistent results with those without an approximation.

8 pages, 13 figures, version accepted for publication in Phys. Rev. D

References in corpus (31)

• High density QCD on a Lefschetz thimble?
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Finite-density lattice QCD and sign problem: current status and open problems
• A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
• The QCD Sign Problem for Small Chemical Potential
• Toward solving the sign problem with path optimization method
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
• Parallel tempering algorithm for integration over Lefschetz thimbles
• Deep Learning Beyond Lefschetz Thimbles
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Application of neural network to sign problem via path optimization method
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
• 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
• Thirring model at finite density in 0+1 dimensions with stochastic quantization: Crosscheck with an exact solution
• Path integral contour deformations for noisy observables
• Worldvolume approach to the tempered Lefschetz thimble method
• A simple approach towards the sign problem using path optimisation
• 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
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• Path optimization for $U(1)$ gauge theory with complexified parameters
• Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
• Gauge invariant input to neural network for path optimization method
• Improving efficiency of the path optimization method for a gauge theory
• Settling an old story: solution of the Thirring model in thimble regularization
• Deep Learning of Fermion Sign Fluctuations
• Convex optimization and contour deformations