Operator entanglement entropy of the time evolution operator in chaotic systems

Understand

We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized and Floquet systems.

• In the random field Heisenberg model we find a universal power law growth of the operator EE at weak disorder, a logarithmic growth at strong disorder, and extensive saturation values in both cases.
• In a Floquet spin model, the saturation value after an initial linear growth is identical to the value of a random unitary operator (the Page value).
• We understand these properties by mapping the operator EE to a global quench problem evolved with a similar parent-Hamiltonian in an enlarged Hilbert space with the same chaotic, MBL and Floquet properties as the original Hamiltonian.