Excited-state quantum phase transitions in systems with two degrees of freedom: Level density,level dynamics,thermal properties

Quantum systems with a finite number of freedom degrees f$f$ develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f$f$, particularly f=2$f=2$, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition.