Holographic complexity of the disk subregion in (2 + 1)-dimensional gapped systems.

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, and (ii) when the entanglement entropy exhibits the classic "swallowtail" phase transition, the complexity is sensitive but reacts differently. [ABSTRACT FROM AUTHOR]