Towards entanglement negativity of two disjoint intervals for a one dimensional free fermion

Understand

We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion.

• By means of a direct calculation based on coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function.
• We show that the moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point.
• These equalities imply the non trivial result that also the negativity of the free fermion and the self-dual boson are equal.