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

•ESQPTs found in infinite-size limit of systems with low numbers of freedom degrees ff.•ESQPTs related to non-analytical evolutions of classical phase–space properties.•ESQPT signatures analyzed for general ff, particularly f=2f=2, extending known case f=1f=1.•ESQPT signatures identified in smoothened density and flow of energy spectrum.•ESQPTs shown to induce a new type of thermodynamic anomalies.

Quantum systems with a finite number of freedom degrees ff 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 ff, particularly f=2f=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.