  Using the volume of the space enclosed by the Ryu-Takayanagi (RT) surface, we
study the complexity of the disk-shape subregion (with radius R) in various
(2+1)-dimensional gapped systems with gravity dual. These systems include a
class of toy models with singular IR and the bottom-up models for quantum
chromodynamics and fractional quantum Hall effects. Two main results are: i) in
the large-R expansion of the complexity, the R-linear term is always absent,
similar to the absence of topological entanglement entropy; ii) when the
entanglement entropy exhibits the classic `swallowtail' phase transition, the
complexity is sensitive but reacts differently.
