Abstract
We study the dynamics of (Rényi) mutual information, logarithmic negativity, and (Rényi) reflected entropy after exciting the ground state by a local operator. Together with recent results from ref. [1], we are able to conjecture a close-knit structure between the three quantities that emerges in states excited above the vacuum, including both local and global quantum quenches. This structure intimately depends on the chaoticity of the theory i.e. there exist distinct sets of equivalences for integrable and chaotic theories. For rational conformal field theories (RCFT), we find all quantities to compute the quantum dimension of the primary operator inserted. In contrast, we find the correlation measures to grow (logarithmically) without bound in all c > 1 conformal field theories with a finite twist gap. In comparing the calculations in the two classes of theories, we are able to identify the dynamical mechanism for the breakdown of the quasi-particle picture in 2D conformal field theories. Intriguingly, we also find preliminary evidence that our general lessons apply to quantum systems considerably distinct from conformal field theories, such as integrable and chaotic spin chains, suggesting a universality of entanglement dynamics in non-equilibrium systems.
Highlights
Entanglement is purely bipartite and carried by local quasi-particle pairs
We study the dynamics of (Rényi) mutual information, logarithmic negativity, and (Rényi) reflected entropy after exciting the ground state by a local operator
For rational conformal field theories (RCFT), we find all quantities to compute the quantum dimension of the primary operator inserted
Summary
The entanglement content of the quasi-particle created by the local operator is the logarithm of the quantum dimension Using this fact and prior results for Rényi mutual information, we are able to confirm (1.7) for RCFT and show that analogous statements for other Rényi entropies would be inconsistent. In the Regge limit, the dominant operator exchange in the cross-channel conformal block is no longer the identity operator, as it was for RCFT This fact essentially destroys the notion of local propagating quasi-particles and leads to logarithmic growth in all correlation measures. To leading order, the backreaction may be accurately accounted for by computing the entanglement wedge cross-section without backreaction [26] Explicit checks of this approximation are few, and we provide the first check for dynamical nonsymmetric spacetimes. We find that while the leading approximation correctly predicts the logarithmic growth of negativity, the overall coefficient is corrected due to the gravitational interactions between a falling particle and the tensionful entanglement wedge cross-section
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