Shenglong Xu, Texas A&M University

"Emergent Symmetry and Scrambling Dynamics of Brownian SYK Models"

Abstract: Quantum information scrambling is closely tied to the operator dynamics and can be quantified by the out-of-time ordered correlator (OTOC). In this talk, I will introduce a new approach to study the scrambling and operator dynamics of the Brownian SYK models for both the Majorana model without charge conservation and the complex model with charge conservation. I will show that in both models there appear emergent symmetry structures after taking random averages of the coupling. The random average maps the operator dynamics of the Majorana model and the complex model to the imaginary time dynamics of an SU(2) spin and an SU(4) spin, respectively, which become solvable in the large N limit. Furthermore, the symmetry structure drastically reduces the size of Hilbert space required to calculate OTOC from exponential to linear in N, providing us full access to the operator dynamics at all times for large but finite N. In the case of the complex model with charge conservation, using this approach, we obtain the OTOC from each charge sector both numerically at finite N and analytically in the large N limit. Based on the results, I will discuss how charge density affects operator dynamics and scrambling. Reference: L. Agarwal, S. Xu, arXiv:2108.05810.