Universality in the tripartite information after global quenches

Abstract

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 $I_3^{(\alpha )}(A,B,C)$. 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 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 $I_3^{(\alpha )}$ in systems that are dual to free fermions, propose a field-theory description, and work out 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 $x\to 1^{-}$, which we call ``residual tripartite information''. If nonzero, our analysis points to a universal residual value $-\log 2$ independently of the Rényi index $\alpha$, and hence applies also to the genuine (von Neumann) tripartite information.

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Cited by in corpus (10)

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• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Entanglement content of kink excitations
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State