  We present the quantum dynamics of a spin coupling to a bath of independent
spins via the dissipaton equation of motion (DEOM) approach. The bath,
characterized by a continuous spectral density function, is composed of spins
that are independent level systems described by the su(2) Lie algebra. This
represents an extreme class of anharmonic environment. Based on the conclusion
drawn by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and Makri [J. Chem.
Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian
environment under its linear response limit, we derive the
fluctuation-dissipation theorem (FDT) of the spin bath from a microscopic
perspective, and generalize the discussion to the case of arbitrary bath spin
quantum number S. Next, the time-domain Prony fitting decomposition scheme is
applied to the bare-bath time correlation function (TCF) given by FDT to
generate the exponential decay basis (or pseudo modes) for DEOM construction.
The accuracy and efficiency of this strategy has been justified by a variety of
numerical results. We envision this work provides new insights to extend the
hierarchical equations of motion (HEOM) and DEOM approach to certain types of
anharmonic enviroments with arbitrary TCF or spectral density
