This article extends our previous analysis Stránský etal. (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.
Bibliographical noteFunding Information:
This work was performed under the project no. P203-13-07117S of the Czech Science Foundation. P.S. acknowledges support by CONACyT and PAPIIT-UNAM, Mexico . A.L. and M.M. appreciate the funding by Israel Science Foundation and the Golda Meir Fellowship .
- Finite-size effects
- Oscillatory component of level density
- Quantum phase transitions
- Regular/chaotic dynamics