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

TL;DR

This paper introduces a non-perturbative theoretical framework to identify and analyze pseudo-Goldstone and slow-Goldstone modes in quantum matter, with implications for quantum chaos and information scrambling.

Contribution

The work develops a novel non-perturbative formalism to detect light and slow Goldstone modes beyond traditional methods, applicable to diverse quantum systems.

Findings

Identification of pseudo-Goldstone and slow-Goldstone modes in superfluids.

Discussion of these modes' roles in quantum information scrambling.

Comparison of slow-Goldstone modes with similar phenomena in SYK models.

Abstract

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.