Many-body entanglement in a topological chiral ladder

We find that the topological phase transition in a chiral ladder is characterized by dramatic signatures in many body entanglement entropy between the legs, close to half filling. The value of entanglement entropy for various fillings close to half filling is identical, at the critical point, but splays out on either side, thus showing a sharp signature at the transition point. A second signature is provided by the change in entanglement entropy when a particle is added (or subtracted) from half filling which turns out to be exactly $\ensuremath{-}log2$ in the trivial phase but zero in the topological phase. A microscopic understanding of tendencies to form singlets along the rungs in the trivial phase, and along the diagonals in the topological phase, is afforded by a study of concurrence. At the topological phase transition the magnitude of the derivative of the average concurrence of all the rungs shows a sharp peak. Also, at the critical point, the average concurrence is the same for various fillings close to half filling but splays out on either side, just like entanglement entropy. Entanglement entropy also offers a striking signature at the vortex-to-Meissner phase transition inherent in this system.