  We analyze the entanglement generation in a pair of qubits that experience
the vacuum fluctuations of a scalar field in the Cosmic String spacetime. The
qubits are modeled as Unruh-DeWitt detectors coupled to a massless scalar
field. We introduce a Heisenberg $XY$-interaction between the qubits that
enhances the generation of quantum correlations. It is supposed that the qubits
begin at a general mixed state described by a density operator with no
entanglement while the field stays at its vacuum state. In this way, we find
the general properties and conditions to create entanglement between the qubits
by exploiting the field vacuum fluctuations. We quantify the qubits
entanglement using the Negativity measure based on the Peres-Horodecki positive
partial transpose criterion. We find that the Cosmic String would increase the
entanglement harvesting when both qubits are near the Cosmic String. When the
qubits locations are far from the Cosmic String we recover the usual results
for Minkowski space. The Heisenberg $XY$-interaction enhance the entanglement
harvesting irrespective of the coupling nature (ferromagnetic or
anti-ferromagnetic). When the qubits are far apart from each other we find a
maximum entanglement harvesting at the resonance points between the Heisenberg
coupling constant and the qubits energy gap.
