Theory Seminar: Dynamical symmetries in Krylov space

Dr. Nicolas Loizeau
Niels Bohr Institute
Quantum Many-Body Seminar, at the Theory Seminar Room
Thursday, March 26, 11:30 CET

For locally interacting closed systems, the dynamics of local observables can be expanded into eigenmodes of the Liouvillian, so-called dynamical symmetries. These operators provide a full characterization of the dynamics of the system. Deriving these operators, apart from a very limited class of models, has not been possible. I will present a method to numerically and analytically derive some of these dynamical symmetries in the thermodynamic limit by introducing a naturally emergent open boundary condition on the Krylov chain. This boundary condition defines a partitioning of the Krylov space into system and environment degrees of freedom, where nonlocal operators make up an effective bath for the local operators. Our approach lets us directly relate the operator growth hypothesis to thermalization and exponential decay of observables in chaotic systems and provides a powerful approach for computing notably challenging many-body dynamics.