  This paper considers a spin chain model by numerically solving the exact
model to explore the non-perturbative dynamical decoupling regime, where an
important issue arises recently (J. Jing, L.-A. Wu, J. Q. You and T. Yu,
arXiv:1202.5056.). Our study has revealed a few universal features of
non-perturbative dynamical control irrespective of the types of environments
and system-environment couplings. We have shown that, for the spin chain model,
there is a threshold and a large pulse parameter region where the effective
dynamical control can be implemented, in contrast to the perturbative
decoupling schemes where the permissible parameters are represented by a point
or converge to a very small subset in the large parameter region admitted by
our non-perturbative approach. An important implication of the non-perturbative
approach is its flexibility in implementing the dynamical control scheme in a
experimental setup. Our findings have exhibited several interesting features of
the non-perturbative regimes such as the chain-size independence, pulse
strength upper-bound, noncontinuous valid parameter regions, etc. Furthermore,
we find that our non-perturbative scheme is robust against randomness in model
fabrication and time-dependent random noise.
