Improving efficiency of the path optimization method for a gauge theory

Abstract

We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the complexified integration path, we employ the path optimization method. The $2$-dimensional $\text{U}(1)$ gauge theory with the complex gauge coupling constant is used as a laboratory to evaluate the efficiency. It is found that the gauge-covariant neural network, which is composed of the Stout-like smearing, can enhance the average phase factor, as the gauge-invariant input does. For the approximation of the Jacobian, we test the most drastic case in which we perfectly drop the Jacobian during the learning process. It reduces the numerical cost of the Jacobian calculation from $\mathcal{O}(N^3)$ to $\mathcal{O}(1)$, where $N$ means the number of degrees of freedom of the theory. The path optimization using this Jacobian approximation still enhances the average phase factor at expense of a slight increase of the statistical error.

8 pages, 5 figures; accepted version

References in corpus (13)

• Tensor renormalization group approach to 2D classical lattice models
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
• Tensor renormalization group study of the non-Abelian Higgs model in two dimensions
• Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density
• Worldvolume approach to the tempered Lefschetz thimble method
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction
• Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Lattice Scalar Field Theory At Complex Coupling
• 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

Cited by in corpus (3)

• Exploring QCD matter in extreme conditions with Machine Learning
• Application of the path optimization method to a discrete spin system
• Path optimization method for the sign problem caused by fermion determinant