In this letter we study the negativity of one dimensional free fermions. We derive the general form of the $\mathbb{ Z}_{ N}$ symmetric term in moments of the partial transposed (reduced) density matrix, which is an algebraic function of the end points of the system. Such a path integral turns out to be a convenient tool for making estimations for the negativity.
Categories: hep-th cond-mat.stat-mech quant-ph