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 $-\log{2}$ 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.