Localization in Lattice Gauge Theory and a New Multigrid Method
Martin B\"aker
TL;DR
This paper demonstrates the strong localization of eigenmodes in a 2D SU(2) Laplace operator and introduces a multigrid method that efficiently handles these localized modes without critical slowing down.
Contribution
It presents a novel multigrid algorithm tailored for localized eigenmodes in lattice gauge theory, improving computational efficiency.
Findings
Eigenmodes are strongly localized in the 2D SU(2) Laplace operator.
The new multigrid method effectively manages localized modes.
No critical slowing down observed with the new algorithm.
Abstract
We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, shows no critical slowing down for this problem.
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