Entanglement entropies (EEs) are an indicator of the complexity in quantum states and of their approximability by matrix product decompositions. I will present results on the evolution of EEs in many-body systems taken out of equilibrium. I will focus on models that can be realized with optically trapped ultracold atoms, and on exotic types of spin-boson models that are relevant for experimental setups with cavity-coupled molecular ensembles.
The interplay between coherent Hamiltonian dynamics and additional dissipation can lead to interesting evolution of entanglement. Recently, we discovered an effect in quenched 1D XXZ spin chains subjected to dephasing noise: There, the operator entanglement (OE), an EE-equivalent for density matrices, initially exhibits an expected rise and fall behavior. However, at long times we find that the OE can rise again, following a universal logarithmic increase. This talk will explain this behavior using a combination of exact numerical results and analytical arguments valid for strong dephasing.
