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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.
We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two or four Gau
We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading orde
We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, texttt{arXiv:1104.1004}, for the reduced density of states of two disjoint intervals with l
We study the time evolution of the logarithmic negativity after a global quantum quench. In a 1+1 dimensional conformal invariant field theory, we consider the negativity between two intervals which can be either adjacent or disjoint. We show that th
The study of the entanglement dynamics plays a fundamental role in understanding the behaviour of many-body quantum systems out of equilibrium. In the presence of a globally conserved charge, further insights are provided by the knowledge of the reso