Universality in the tripartite information after global quenches

Vanja Marić, Maurizio Fagotti

Published 2022-09-28Version 1

We consider macroscopically large 3-partitions $(A,B,C)$ of connected subsystems $A\cup B \cup C$ in infinite spin chains and study the R\'enyi-$\alpha$ tripartite information $I_3^{(\alpha)}(A,B,C)$. 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 $I_3^{(\alpha)}(A,B,C)$ is known to be a universal function of the cross ratio $x=|A||C|/[(|A|+|B|)(|C|+|B|)]$, where $|A|$ denotes $A$'s length. We identify three classes of states for which time evolution under translationally invariant Hamiltonians can build up (R\'enyi) tripartite information with a universal dependency on $x$. We report a numerical study of $I_3^{(\alpha)}$ in systems that are dual to free fermions, propose a field-theory description, and conjecture their asymptotic behaviour for $\alpha=2$ in general and for generic $\alpha$ in a subclass of systems. This allows us to infer the value of $I_3^{(\alpha)}$ in the scaling limit $x\rightarrow 1^-$, which we call "residual tripartite information". If nonzero, our analysis points to a universal residual value $-\log 2$ independently of the R\'enyi index $\alpha$, and hence applies also to the genuine (von Neumann) tripartite information.