Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star

Interacting central spin systems, in which a is coupled to strongly correlated bath with intrabath interaction, consist of an important class systems beyond the usual Gaudin magnet. These are relevant several realistic setups and serve as interesting platform study interaction controlled decoherence frustration induced instability magnetic order. Using equations-of-motion method based on analytical representations spin-operator matrix elements XX chain, we obtain exact long-time dynamics generalized Heisenberg star consisting spin-$S$ inhomogeneously XXZ chain $N\ensuremath{\le}16$ spins. In contrast previous studies where mainly concerned, focus influence orders within bath. By preparing N\'eel state, find that gapless phase even weak system-bath coupling could lead nearly perfect relaxation antiferromagnetic gapped phase, staggered magnetization decays rapidly approaches steady value increases increasing anisotropy parameter. findings suggest possibility controlling internal many-spin by certain auxiliary few degrees freedom. We also R\'enyi entanglement entropy when prepared ground state. Both overall profile initial growth rate found exhibit minima at critical point