Abstract
We consider the R\'enyi-α tripartite information I₃^(α) of three adjacent subsystems in the stationary state emerging after global quenches in noninteracting spin chains from both homogeneous and bipartite states. We identify settings in which I₃^(α) remains nonzero also in the limit of infinite lengths and develop an effective quantum field theory description of free fermionic fields on a ladder. We map the calculation into a Riemann-Hilbert problem with a piecewise constant matrix for a doubly connected domain. We find an explicit solution for α=2 and an implicit one for α>2. In the latter case, we develop a rapidly convergent perturbation theory that we use to derive analytic formulae approximating I₃^(α) with outstanding accuracy.