High Energy Theory Group Meeting: Krylov complexity in quantum field theory and beyond

Abstract: 

I will describe recent attempts to use dynamics in Krylov space to characterize behavior of quantum chaotic systems. First, I will review basics of the Krylov space (recursion) method and how it is related to completely integrable systems. Then I will formulate several hypothesis outlining universality of Krylov dynamics, in particular Krylov complexity, for the chaotic systems. In the second part of the talk I will consider several examples of quantum field theories, calculate for them growth of Krylov complexity and argue it is not a credible signature of chaos. 

Seminar Organizer: Andrea Guerrieri