Local Quenches from a Krylov Perspective
Giuseppe Di Giulio (Stockholm University)
In the last few years, quantifying the complexity of quantum states has found applications in many fields, including quantum information and computing, quantum dynamics in many-body systems, and black hole physics. Among these measures, the spread complexity roughly quantifies the size of the space of states visited along quantum dynamics. It is obtained through Krylov space methods, which consist of projecting the evolution of a state onto one-dimensional dynamics. In this talk, I will discuss the evolution of the spread complexity after a local quantum quench in conformal field theories (CFT). Interestingly, this quantity depends on the central charge of the considered theory. I will also show that, to get rid of all the non-universal contributions in the leading time behaviour, it is convenient to study another Krylov space quantity, the K-entropy, an entropy measure defined for pure states without the need for a bipartition. These results support the usefulness of the Krylov space methods to study quantum dynamics