Pérez Fernández, P.Relaño Pérez, ArmandoCejnar, P.Arias, J. M.Dukelsky, J.García Ramos, J. E.2023-06-202023-06-202012978-0-7354-1100-510.1063/1.4759413https://hdl.handle.net/20.500.14352/45629© American Institute of Physics (AIP). Meeting on Beauty in Physics - Theory and Experiment in Honor of Francesco Lachello on the Occasion of his 70th Birthday (2012. Hacienda Cocoyoc, Mexico). This work is presented on the occasion of Franco Iachello’s 70th birthday. This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación and FEDER funds under projects FIS2011-28738-c02-01. Spanish Consolider Ingenio Programme CPAN - CSD2007-00042 and by Junta de Andalucía FQM-160 and P07-FQM-02894.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.engbook parthttp://dx.doi.org/10.1063/1.4759413http://scitation.aip.orgopen access536Quantum chaosExcited state quantum phase transitionFísica (Física)22 Física