  Decoherence of a central spin coupled to an interacting spin bath via
inhomogeneous Heisenberg coupling is studied by two different approaches,
namely an exact equations of motion (EOMs) method and a Chebyshev expansion
technique (CET). By assuming a wheel topology of the bath spins with uniform
nearest-neighbor $XX$-type intrabath coupling, we examine the central spin
dynamics with the bath prepared in two different types of bath initial
conditions. For fully polarized baths in strong magnetic fields, the
polarization dynamics of the central spin exhibits a collapse-revival behavior
in the intermediate-time regime. Under an antiferromagnetic bath initial
condition, the two methods give excellently consistent central spin decoherence
dynamics for finite-size baths of $N\leq14$ bath spins. The decoherence factor
is found to drop off abruptly on a short time scale and approach a finite
plateau value which depends on the intrabath coupling strength
non-monotonically. In the ultrastrong intrabath coupling regime, the plateau
values show an oscillatory behavior depending on whether $N/2$ is even or odd.
The observed results are interpreted qualitatively within the framework of the
EOM and perturbation analysis. The effects of anisotropic spin-bath coupling
and inhomogeneous intrabath bath couplings are briefly discussed. Possible
experimental realization of the model in a modified quantum corral setup is
suggested.
