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Quantum quenches to or near criticality give rise to the phenomenon of\textit{aging}, manifested by glassy-like dynamics at short times and far fromequilibrium. The recent surge of interest in the dynamics of quantum many-bodysystems has rejuvenated interest in this phenomenon. Motivated by theubiquitous long-range interactions in emerging experimental platforms, it isvital to study quantum aging in such settings. In this work, we investigate thedynamical universality and aging in the $d$-dimensional $O(N)$ model with thelong-range coupling $1/x^{d+\sigma}$ and in the mean-field limit $N\to\infty$that allows an exact treatment. An immediate consequence of long-range couplingis the emergence of nonlinear light cones. We focus on the correlation andresponse functions, and identify a rich scaling behavior depending on how thecorresponding space-time positions are located relative to each other, via a\textit{local light cone}, and to the time of the quench via a global\textit{quench light cone}. We determine the initial-slip exponent that governsthe short-time dependence of two-point functions. We highlight the newqualitative features of aging due to the long-range coupling, in particular inthe region outside the light cones. As an important consequence of long-rangecoupling, the correlation function decays as $1/x^{d+\sigma}$ outside thequench light cone while increasing polynomially with the total time afterquench. This is while, for short time differences, the two-time responsefunction "equilibrates" at \textit{all} distances even outside this light cone.Our analytic findings are in excellent agreement with exact numerics, andprovide a useful benchmark for modern experimental platforms with long-rangeinteractions.

Quantum aging and dynamical universality in the long-range $O(N\to\infty)$ model