Excited-state quantum phase transitions in systems with two degrees of freedom: II. Finite-size effects

•Oscillatory components of state density and spectral flow studied near ESQPTs.•Enhanced finite-size precursors of ESQPT caused by fully/partly separable dynamics.•These precursors appear due to criticality of a subsystem with lower dimension.•Separability-induced finite-size effects disappear in case of fully chaotic dynamics.

This article extends our previous analysis Stránský et al. (2014) of Excited-State Quantum Phase Transitions (ESQPTs) in systems of dimension two. We focus on the oscillatory component of the quantum state density in connection with ESQPT structures accompanying a first-order ground-state transition. It is shown that a separable (integrable) system can develop rather strong finite-size precursors of ESQPT expressed as singularities in the oscillatory component of the state density. The singularities originate in effectively 1-dimensional dynamics and in some cases appear in multiple replicas with increasing excitation energy. Using a specific model example, we demonstrate that these precursors are rather resistant to proliferation of chaotic dynamics.