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Overview : https://indico.cern.ch/event/1514154/overview

The late-time dynamics of many-body systems is one of the central problems in statistical mechanics. The eventual emergence of Gibbs ensembles at late times for closed systems is usually explained using the Eigenstate Thermalization Hypothesis (ETH): it postulates, among other things, local indistinguishability of the energy eigenstates and proper statistical ensembles. Rare eigenstates that violate ETH are known as many-body scars and can affect the dynamics of the system in a non-trivial way.

We investigate a related mechanism for an open quantum many-body system. In particular, we focus on a model that hosts, together with the infinite-temperature state, another additional stationary state. The latter is exceptional in many respects and plays the role of a quantum scar. We discuss the properties of the model, focusing on the fate of interfaces between the two states. We find that at late times an effective description is based on stochastic fluctuations of the interface; in particular, the scar is progressively eroded at a finite velocity, and the interface broadens diffusively. While this mechanism resembles hydrodynamics of local conserved charges, important differences are pointed out.

This is a joint work with Alice Marché, Gianluca Morettini, Leonardo Mazza, and Lorenzo Gotta.

Ref. [arxiv:2412.13820], accepted on Physical Review Letter.

Abstract: Microcausality states that field operators commute at spacelike separations. While this property holds directly for Lorentz-invariant states, it becomes more subtle when Lorentz symmetry is spontaneously broken. In this talk, I analyze the operatorial commutator in interacting scalar field theories using the interaction picture formalism. For theories without derivative interactions, I show that microcausality is preserved, ensuring that the interacting commutator still vanishes outside the standard Minkowski light cone, regardless of the state considered. In contrast, derivative interactions modify the free-theory commutator by introducing corrections proportional to derivatives of delta functions, evaluated on the light cone of the free theory. When expectation values are taken, these corrections cancel in Lorentz-invariant states but persist in states where Lorentz symmetry is spontaneously broken. I show that these terms are the signal of a perturbative shift in the light-cone structure of the free theory, due to interactions. Finally, I discuss what goes wrong with the standard argument according to which Lorentz invariance implies microcausality.

Using necessary and sufficient conditions for the saturation of the Araki-Lieb (AL) and related  inequalities which are realized holographically in black hole geometries, we prove that a typical pure state in a large N holographic CFT has two associated length scales that are determined only by the energy and conserved charges; one of them is a microscopic length scale L_{UV}, and the other is an infrared length scale L_{H} > L_{UV}.  Furthermore, the degrees of freedom between these two length scales are effectively split into two factors, one purifying the degrees of freedom at length scales smaller than L_{UV} and the other purifying those at length scales larger than L_{H}. Remarkably, the pure state factor involving the ultraviolet degrees of freedom is state independent. We also find precisely how deviations from this architecture are exponentially suppressed by studying quantum mutual information of two non-overlapping regions. Our results imply that all black holes can be isolated from the asymptotic region by a well-defined hypersurface which is the envelope of all critical entanglement wedges for which AL is saturated, and the split property emerges in the region bounded by this hypersurface and the horizon.

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