  Spatially resolved images of debris disks frequently reveal complex
morphologies such as gaps, spirals, and warps. Most existing models for
explaining such morphologies focus on the role of massive perturbers (i.e.
planets, stellar companions), ignoring the gravitational effects of the disk
itself. Here we investigate the secular interaction between an eccentric planet
and a massive, external debris disk using a simple analytical model. Our
framework accounts for both the gravitational coupling between the disk and the
planet, as well as the disk self-gravity -- with the limitation that it ignores
the non-axisymmetric component of the disk (self-)gravity. We find generally
that even when the disk is less massive than the planet, the system may feature
secular resonances within the disk (contrary to what may be naively expected),
where planetesimal eccentricities get significantly excited. Given this outcome
we propose that double-ringed debris disks, such as those around HD 107146 and
HD 92945, could be the result of secular resonances with a yet-undetected
planet interior to the disk. We characterize the dependence of the properties
of the secular resonances (i.e. locations, timescales, and widths) on the
planet and disk parameters, finding that the mechanism is robust provided the
disk is massive enough. As an example, we apply our results to HD 107146 and
find that this mechanism readily produces $\sim 20$ au wide non-axisymmetric
gaps. Our results may be used to set constraints on the total mass of
double-ringed debris disks. We demonstrate this for HD 206893, for which we
infer a disk mass of $\approx 170$ Earth masses by considering perturbations
from the known brown dwarf companion.
