We consider macroscopically large 3-partitions $(A,B,C)$ of connected subsystems $A\cup B\cup C$ in infinite quantum spin chains and study the Rényi-$\alpha$ tripartite information $I_3^{\left(\alpha \right)}(A,B,C)$. At equilibrium in clean 1D systems with local Hamiltonians it generally vanishes. A notable exception is the ground state of conformal critical systems, in which $I_3^{\left(\alpha \right)}(A,B,C)$ is known to be a universal function of the cross ratio $x=\left|A\right|\left|C\right|/\left[\right(\left|A\right|+\left|B\right|\left)\right(\left|C\right|+\left|B\right|\left)\right]$, where $\left|A\right|$ denotes $A$'s length. We identify different classes of states that, under time evolution with translationally invariant Hamiltonians, locally relax to states with a nonzero (Rényi) tripartite information, which furthermore exhibits a universal dependency on $x$. We report a numerical study of $I_3^{\left(\alpha \right)}$ in systems that are dual to free fermions, propose a field-theory description, and work out their asymptotic behavior for $\alpha =2$ in general and for generic $\alpha$ in a subclass of systems. This allows us to infer the value of $I_3^{\left(\alpha \right)}$ in the scaling limit $x\to 1^{-}$, which we call “residual tripartite information”. If nonzero, our analysis points to a universal residual value $-log2$ independently of the Rényi index $\alpha$, and hence applies also to the genuine (von Neumann) tripartite information.

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• Entanglement measures
• Quantum quench
• Quantum statistical mechanics
• 1-dimensional spin chains
• Nonequilibrium systems
• Quantum spin models
• Conformal field theory
• Duality
• Effective field theory
• Exact solutions for many-body systems
• Integrable systems
• Quantum spin chains
• Replica methods
• Spin ladders