  Extended gaps in the debris disks of both Vega and Fomalhaut have been
observed. These structures have been attributed to tidal perturbations by
multiple super-Jupiter gas giant planets. Within the current observational
limits, however, no such massive planets have been detected. Here we propose a
less stringent `lone-planet' scenario to account for the observed structure
with a single eccentric gas giant and suggest that clearing of these wide gaps
is induced by its sweeping secular resonance. During the depletion of the disk
gas, the planet's secular resonance propagates inward and clears a wide gap
over an extended region of the disk. Although some residual intermediate-size
planetesimals may remain in the gap, their surface density is too low to either
produce super-Earths or lead to sufficiently frequent disruptive collisions to
generate any observable dusty signatures. The main advantage of this
lone-planet sweeping-secular-resonance model over the previous multiple gas
giant tidal truncation scenario is the relaxed requirement on the number of gas
giants. The observationally inferred upper mass limit can also be satisfied
provided the hypothetical planet has a significant eccentricity. A significant
fraction of solar or more massive stars bear gas giant planets with significant
eccentricities. If these planets acquired their present-day kinematic
properties prior to the depletion of their natal disks, their sweeping secular
resonance would effectively impede the retention of neighboring planets and
planetesimals over a wide range of orbital semi-major axes.
