Localization dynamics in a centrally coupled system

In systems where interactions couple a central degree of freedom and bath, one would expect signatures the bath's phase to be reflected in dynamics freedom. This has been recently explored connection with many-body localized baths coupled qubit or single cavity mode -- growing experimental relevance various platforms. Such models also have an interesting Floquet localization via quantizing external drive, although this relatively unexplored. Here we adapt multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method, well-known tree tensor network algorithm, numerically simulate freedom, represented by $d$-level system (qudit), disordered interacting 1D spin bath. ML-MCTDH allows us reach $\approx 10^2$ lattice sites, far larger size than what is feasible exact diagonalization kernel polynomial methods. From intermediate time dynamics, find well-defined thermodynamic limit for qudit upon appropriate rescaling system-bath coupling. The shows similar scaling collapse Edward-Anderson glass order parameter entanglement entropy at short times. At longer scales, see slow growth entanglement, which may arise from dephasing mechanisms long-range mediated Similar signs are shown appear as well unscaled