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

TL;DR

This paper investigates the holographic complexity of disk-shaped subregions in (2+1)-dimensional gapped systems using the volume enclosed by the RT surface, revealing the absence of R-linear terms and the complexity's response to phase transitions.

Contribution

It introduces a study of holographic complexity in gapped systems, highlighting the absence of R-linear terms and the complexity's behavior during phase transitions.

Findings

R-linear term in complexity expansion is absent.

Complexity reacts differently during entanglement entropy phase transitions.

Complexity behavior parallels topological entanglement entropy absence.

Abstract

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.