Opening Krylov space to solve long time dynamics via dynamical symmetries
Nicolas Loizeau (Copenhagen)
Solving long time dynamics of closed quantum many-body systems is one of the main challenges of the field. For locally interacting closed systems, the dynamics of local observables can always be expanded into (pseudolocal) eigenmodes of the thermodynamic Liouvillian, so called dynamical symmetries. These dynamical symmetries come in two classes – transient operators, which decay in time and perpetual operators, which either oscillate forever or stay the same (conservation laws). These operators provide a full characterization of short and long time dynamics of the system.
I will present a method to numerically and analytically derive some of these dynamical symmetries in infinite closed systems 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 non-local operators make up an effective bath for the local operators.
We demonstrate the practicality of the method on some numerical examples and derive analytical results in two idealized cases. Our approach lets us directly relate the operator growth hypothesis to thermalization and exponential decay of observables in chaotic systems.