In this work, we develop a nonperturbative theory to identify a light pseudo-Goldstone mode with a small mass, as well as a type of Goldstone mode with a tiny slope (termed the slow-Goldstone mode), which may not be obtained via traditional perturbative methods. We demonstrate our formalism in the context of superfluids formed by Rashba spin-orbit coupled spinor bosons in a square lattice weakly interacting with a spin-anisotropic interaction. The experimental detections of these two modes, especially their roles leading to the quantum information scramblings at a finite temperature are discussed. The slow-Goldstone mode is compared with the slow light and the soft mode in the Sachdev-Ye-Kitaev models. This nonperturbative formalism can be widely applied to study other emergent particles in various quantum matter.

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• Nonperturbative effects in field theory
• Perturbation theory
• Quantum field theory (low energy)
• Bose-Einstein condensates