Krylov Complexity as a Probe for Chaos

• Mohammad Javad Vasli (School of Nano Science, IPM)

In this talk, I will explore the use of Krylov complexity as a diagnostic tool for understanding the chaotic nature of quantum systems. The concept of Krylov complexity is introduced within the framework of the Lanczos algorithm, allowing us to study the system's dynamics in a finite Krylov subspace. By analyzing the time evolution and saturation of complexity, it is possible to demonstrate how it distinguishes between chaotic and integrable many-body systems. These distinctions will be illustrated with numerical results from spin models, providing insights into the interplay between Krylov complexity and quantum chaos.