How does information propagate in quantum systems?
The out-of-equilibrium dynamics of strongly correlated quantum systems have become a central topic for basic quantum science and applications to emerging quantum technologies, driven by advances in time-dependent control of artificial quantum matter. However, fundamental questions persist—particularly regarding how information propagates such systems. Here, we show that this challenge gives rise to intricate, largely unexplored dynamical behaviors. We develop a general microscopic framework to characterize the generic dynamics of lattice models, encompassing both short- and long-range interactions. Our analysis uncovers a striking twofold cone-like structure in space-time correlations. In long-range systems, we find that the outer cone exhibits sub-ballistic propagation, while its internal dynamics can transition between ballistic and super-ballistic regimes, depending on the presence or absence of a spectral gap. Crucially, we demonstrate that the structure of these space-time correlation patterns encodes complete information about the elementary excitations of the system. Building on this insight, we introduce a novel spectroscopy method based on quench dynamics. We validate its broad applicability across diverse systems—including those with short- and long-range interactions, as well as disordered systems—through quasi-exact numerical simulations using tensor network approaches. Our results not only confirm the analytical predictions but also highlight the remarkable robustness of quench spectroscopy as a powerful experimental tool to probe the properties of correlated quantum matter.”
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