Krylov fractality and complexity in generic random matrix ensembles

Understand

Krylov space methods provide an efficient framework for analyzing the dynamical aspects of quantum systems, with tridiagonal matrices playing a key role.

• Despite their importance, the behavior of such matrices from chaotic to integrable states, transitioning through an intermediate phase, remains unexplored.
• We aim to fill this gap by considering the properties of the tridiagonal matrix elements and the associated basis vectors for appropriate random matrix ensembles.
• We utilize the Rosenzweig-Porter model as our primary example, which hosts a fractal regime in addition to the ergodic and localized phases.