Abstract
We study the gauge cooling technique for the complex Langevin method applied to the computation in lattice quantum chromodynamics. We propose a new solver of the minimization problem that optimizes the gauge, which does not include any parameter in each iteration, and shows better performance than the classical gradient descent method especially when the lattice size is large. Two numerical tests are carried out to show the effectiveness of the new algorithm.
Highlights
Lattice QCD is the standard nonperturbative tool for quantum chromodynamics (QCD)
We study the gauge cooling technique for the complex Langevin method applied to the computation in lattice quantum chromodynamics
We propose a new solver of the minimization problem that optimizes the gauge, which does not include any parameter in each iteration, and shows better performance than the classical gradient descent method especially when the lattice size is large
Summary
Lattice QCD is the standard nonperturbative tool for quantum chromodynamics (QCD). The link variables. The gauge cooling method utilizes the redundant degrees of freedom in the gauge field, and it does not introduce any biases to the expectation values Such a method has been formally justified in [10,15], and it has been successfully applied to a number of problems [16,17]. The gauge cooling method requires to choose an optimal gauge for the complexified field, which minimizes the distance between the current field and SUð3Þ. In one dimension, it has been figured out in [18] that the problem can be solved analytically since the field is essentially equivalent to the one-link model.
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