  In this letter, we revisit the IEQ method and provide a new perspective on
its ability to preserve the original energy dissipation laws. The invariant
energy quadratization (IEQ) method has been widely used to design energy stable
numerical schemes for phase-field or gradient flow models. Although there are
many merits of the IEQ method, one major disadvantage is that the IEQ method
usually respects a modified energy law, where the modified energy is expressed
in the auxiliary variables. Still, the dissipation laws in terms of the
original energy are not guaranteed. Using the widely-used Cahn-Hilliard
equation as an example, we demonstrate that the Runge-Kutta IEQ method indeed
can preserve the original energy dissipation laws for certain situations up to
arbitrary high-order accuracy. Interested readers are highly encouraged to
apply our idea to other phase-field equations or gradient flow models.
