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We investigate the stationary and dynamical behavior of an Anderson localizedchain coupled to a single central bound state. The coupling to the central sitepartially dilutes the Anderson localized peak towards the nearly resonantsites. In particular, the number of resonantly coupled sites remains finite inthe thermodynamic limit. This is further supported by a multifractal analysisof eigenstates that shows the frozen spectrum of fractal dimension, which ischaracteristic for localized phases in models with power-law hopping. Althoughthe well-known Fano-resonance problem is seemingly similar to our system, itfails to describe it because of the absence of level repulsion within theenergy spectrum. For weak coupling strengths to the central site, we identify aregime with a logarithmic in time transport of particles and information.

Non-interacting central site model: localization and logarithmic entanglement growth