Krylov Localization and suppression of complexity

Understand

Quantum complexity, suitably defined, has been suggested as an important probe of late-time dynamics of black holes, particularly in the context of AdS/CFT.

• A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution.
• Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones.
• In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems.