Exploring the effect of noise on (polyfractal) driving to create multiple symmetries in many-body quantum systems

Symmetries (and their spontaneous rupturing) can be used to protect and engender novel quantum phases and lead to interesting collective phenomena. In [1], the authors described a general dynamical decoupling (“polyfractal”) protocol that can be used to dynamically engineer multiple discrete symmetries in many-body systems. The present work expands on [1] by studying the effect of noise on such a dynamical scheme. To make the analysis tractable, and numerical simulations efficient, we insert errors in the pattern of a Fibonacci replacement sequence. We find generically that the scheme yields symmetries that are protected up to exponentially long times in the inverse error rate. We also discuss how such symmetries can be engineered to protect quantum information and the affect of noise using this scheme.



1. K. Agarwal, I. Martin, Dynamical enhancement of symmetries in many-body systems, Phys Rev. Lett. 125, 080602 (2020)