Universality in the tripartite information after global quenches

Abstract

We consider macroscopically large 3-partitions $(A,B,C)$ of connected subsystems $A\ensuremath{\cup}B\ensuremath{\cup}C$ in infinite quantum spin chains and study the R\'enyi-$\ensuremath{\alpha}$ tripartite information ${I}_{3}^{(\ensuremath{\alpha})}(A,B,C)$. 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 ${I}_{3}^{(\ensuremath{\alpha})}(A,B,C)$ 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 different classes of states that, under time evolution with translationally invariant Hamiltonians, locally relax to states with a nonzero (R\'enyi) tripartite information, which furthermore exhibits a universal dependency on $x$. We report a numerical study of ${I}_{3}^{(\ensuremath{\alpha})}$ in systems that are dual to free fermions, propose a field-theory description, and work out their asymptotic behavior for $\ensuremath{\alpha}=2$ in general and for generic $\ensuremath{\alpha}$ in a subclass of systems. This allows us to infer the value of ${I}_{3}^{(\ensuremath{\alpha})}$ in the scaling limit $x\ensuremath{\rightarrow}{1}^{\ensuremath{-}}$, which we call ``residual tripartite information''. If nonzero, our analysis points to a universal residual value $\ensuremath{-}log2$ independently of the R\'enyi index $\ensuremath{\alpha}$, and hence applies also to the genuine (von Neumann) tripartite information.

Topics & Concepts