Universality in the tripartite information after global quenches: (generalised) quantum XY models

Abstract

We consider the Rényi-α tripartite information {I}_3^{left(alpha right)} 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 {I}_3^{left(alpha right)} 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 {I}_3^{left(alpha right)} with outstanding accuracy.