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We take the paradigm of interacting spin chains, the Heisenbergspin-$\frac{1}{2}$ XXZ model, as a reference system and consider interactingmodels that are related to it by Jordan-Wigner transformations and restrictionsto sub-chains. An example is the fermionic analogue of the gapless XXZHamiltonian, which, in a continuum scaling limit, is described by the masslessThirring model. We work out the R\'enyi-$\alpha$ entropies of disjoint blocksin the ground state and extract the universal scaling functions describing theR\'enyi-$\alpha$ tripartite information in the limit of infinite lengths. Weconsider also the von Neumann entropy, but only in the limit of large distance.We show how to use the entropies of spin blocks to unveil the spin structuresof the underlying massless Thirring model. Finally, we speculate about thetripartite information after global quenches and conjecture its asymptoticbehaviour in the limit of infinite time and small quench. The resultingconjecture for the ``residual tripartite information'', which corresponds tothe limit in which the intervals' lengths are infinitely larger than their(large) distance, supports the claim of universality recently made studyingnoninteracting spin chains. Our mild assumptions imply that the residualtripartite information after a small quench of the anisotropy in the gaplessphase of XXZ is equal to $-\log 2$.

Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium