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The description of strongly-correlated quantum many-body systems far-fromequilibrium is intrinsically challenging due to the amount of information itrequires. We introduce a generalization of the Jastrow ansatz fortime-dependent wavefunctions, that provides an efficient and exact descriptionof the time-evolution of a variety of systems exhibiting strong correlations.Exact solutions previously known are characterized by scale invariance, makingthe evolution of local correlations, such as the spatial density, self-similar.However, we find that a complex-valued time-dependent Jastrow ansatz (TDJA) isnot restricted to scale-invariance and can describe processes lacking it. Theassociated time evolution is equivalent to the implementation of a shortcut toadiabaticity (STA) by counterdiabatic driving along a continuous manifold ofquantum states described by a real-valued TDJA. Thus, our results provide themeans to engineer exact STA in strongly-correlated many-body quantum systemslacking scale invariance. We illustrate our findings in systems withinverse-square interactions, such as the Calogero-Sutherland and the hyperbolicmodels, that are supplemented with pairwise logarithmic interactions. Wefurther consider the dynamics of bosons subject to both contact and Coulombinteractions in one dimension, known as the long-range Lieb-Liniger model. Ourresults can be used to study the quench dynamics in all these models. Ourfindings provide a benchmark for numerical and quantum simulations ofnonequilibrium strongly-correlated systems with continuous variables.

Exact Quantum Dynamics, Shortcuts to Adiabaticity, and Quantum Quenches in Strongly-Correlated Many-Body Systems: The Time-Dependent Jastrow Ansatz