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We theoretically investigate the impact of the excited state quantum phasetransition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Usinga time dependent protocol, we continuously change a model parameter and thendiscuss the scaling properties of the system especially close to the excitedstate quantum phase transition where we find that these depend on the energyeigenstate. On top, we show that the mean-field dynamics with the timedependent protocol gives the correct scaling and expectation values in thethermodynamic limit even for the excited states.

Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model