Gauge invariant input to neural network for path optimization method

Abstract

We investigate the efficiency of a gauge invariant input to a neural network for the path optimization method. While the path optimization with a completely gauge-fixed link-variable input has successfully tamed the sign problem in a simple gauge theory, the optimization does not work well when the gauge degrees of freedom remain. We propose to employ a gauge invariant input, such as plaquette, to overcome this problem. The efficiency of the gauge invariant input to the neural network is evaluated for the 2-dimensional $U(1)$ gauge theory with a complex coupling. The average phase factor is significantly enhanced by the path optimization with the plaquette input, indicating good control of the sign problem. It opens a possibility that the path optimization is available to complicated gauge theories, including Quantum Chromodynamics, in a realistic setup.

arXiv comment7 pages, 8 figures; published version

References in corpus (35)

• Tensor renormalization group approach to 2D classical lattice models
• High density QCD on a Lefschetz thimble?
• Simulating full QCD at nonzero density using the complex Langevin equation
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Toward solving the sign problem with path optimization method
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• Lattice gauge equivariant convolutional neural networks
• Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Application of neural network to sign problem via path optimization method
• Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation
• Applying Complex Langevin Simulations to Lattice QCD at Finite Density
• Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density
• 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
• An improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
• Worldvolume approach to the tempered Lefschetz thimble method
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
• A simple approach towards the sign problem using path optimisation
• Deconfinement transition line with the Complex Langevin equation up to $\mu /T\sim 5$
• 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
• Complex Langevin calculations in QCD at finite density
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• Modifying partition functions: a way to solve the sign problem
• Path optimization for $U(1)$ gauge theory with complexified parameters
• Simulating Yang-Mills theories with a complex coupling
• Perturbative Removal of a Sign Problem
• Complex Paths Around The Sign Problem
• Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm

Cited by in corpus (5)

• Exploring QCD matter in extreme conditions with Machine Learning
• Fourier-Flow model generating Feynman paths
• Improving efficiency of the path optimization method for a gauge theory
• Application of the path optimization method to a discrete spin system
• Path optimization method for the sign problem caused by fermion determinant