Nonperturbative quantum field theory for pseudo-Goldstone modes, slow-Goldstone modes, and their quantum chaos

In this work, we develop a novel form of non-perturbative theory to identify a light pseudo-Goldstone mode with a small mass, as well as a new 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 non-perturbative formalism can be widely applied to study other emergent particles in various quantum matter.