Title : 
Operator Dynamics beyond Scrambling Time using Krylov Complexity 

Speaker  :  Ritam Sinha , King's College, London 
Date  :  January 09, 2023 
Time  :  3:30 PM 
Venue  :  seminar room 3307 
Abstract  : 
Dynamical probes in chaotic quantum systems such as the outoftimeorderedcorrelators ( or OTOCs) can diagnose growth of local operators only up to scrambling times t~ log(S), where S is the system entropy. However, independent estimates for randomisation of quantum states in the Hilbert space requires the much longer Heisenberg time scale tH~exp(S). We study the evolution of operator complexity between these two vastly different time scales using the notion of Krylov complexity. This notion measures growth of operator complexity in a specially designed operator basis called the Krylovbasis, for exponentially long time scales. Using ETH we argue that Krylov complexity in fast scramblers tends to slow down from an exponential to a linear law beyond scrambling time. We also introduce the notion of Krylov entropy to characterise how an initially localised operator randomises over the operator basis, leading to a complete scrambling of the information in the quantum system. 