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We examine how the presence of an excited state quantum phase transitionmanifests in the dynamics of a many-body system subject to a sudden quench.Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state ofthe ferromagnetic phase, we demonstrate that the work probability distributiondisplays non-Gaussian behavior for quenches in the vicinity of the excitedstate critical point. Furthermore, we show that the entropy of the diagonalensemble is highly susceptible to critical regions, making it a robust andpractical indicator of the associated spectral characteristics. We assess therole that symmetry breaking has on the ensuing dynamics, highlighting that itseffect is only present for quenches beyond the critical point. Finally, we showthat similar features persist when the system is initialized in an excitedstate and briefly explore the behavior for initial states in the paramagneticphase.

Work statistics and symmetry breaking in an excited state quantum phase transition