  An external drive can improve the coherence of a quantum many-body system by
averaging out noise sources. It can also be used to realize models that are
inaccessible in the static limit, through Floquet Hamiltonian engineering. The
full possibilities for combining these tools remain unexplored. We develop the
requirements needed for a pulse sequence to decouple a quantum many-body system
from an external field without altering the intended dynamics. Demonstrating
this technique experimentally in an ion-trap platform, we show that it can
provide a large improvement to coherence in real-world applications. Finally,
we engineer an approximate quantum simulation of the Haldane-Shastry model, an
exactly solvable paradigm for long-range interacting spins. Our results expand
and unify the quantum simulation toolbox.
