Entanglement entropy and computational complexity of the driven Anderson impurity model

We do a follow up study of the growth of entanglement entropy and bond dimension in the density matrix renormalization group studies of the Anderson impurity models. We focus on the periodically driven single-impurity Anderson model in real time and applied our previously developed 4-MPS method to do the simulation. In the energy-ordered bath orbital arrangement, we find a critical driving period $T_c$, longer than which the system takes exponential time and shorter than which the system takes polynomial time to simulate. The transition was understood by the Floquet Hamiltonian of the driven system and was found to agree with our previous finding. For the interacting model, the exponential difficulty encountered when $T>T_c$ remains when the bath orbitals are reordered by the quasi-energies of the bath orbitals in the Floquet theory.