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Recently synthetic gauge fields have been implemented on quantum simulators. Unlike the gauge fields in the real world, in synthetic gauge fields, the gauge charge can fluctuate and gauge invariance can be violated, which leads to rich physics unexplored before. In this work, we first propose the gauge violation spectroscopy as a powerful experimentally accessible measurement of synthetic gauge theories. We show that the gauge violation spectroscopy exhibits no dispersion. Using three models as examples, two of which can be exactly solved by bosonization, and one that has been realized in experiment, we further demonstrate the gauge violation spectroscopy can be used to detect the confinement and deconfinement phases. In the confinement phase, it shows a δ-function behavior, while in the deconfinement phase, it has a finite width. Published by the American Physical Society 2024
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