Excited state quantum phase transitions and chaos in the Dicke model

In this contribution, the critical behavior of excited state quantum phase transitions (ESQPT's) and its relation to order and chaos in the Dicke model are studied. This model is non-integrable. For comparison, the same problem is studied for the Jaynes-Cummings model which is, somehow, the integrable version of the Dicke model. The existence of an ESQPT is confirmed in both cases. However, in the Dicke model the signatures of criticality in excited states are blurred by the onset of quantum chaos. It is concluded that the order-to-chaos transition just below the critical energy gives us a chance to study the impact of chaotic dynamics on the signatures of ESQPTs