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

Pavel Stránský, Michal Macek, Amiram Leviatan, Pavel Cejnar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


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.

Original languageAmerican English
Pages (from-to)57-82
Number of pages26
JournalAnnals of Physics
StatePublished - 1 May 2015

Bibliographical note

Funding 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 .

Publisher Copyright:
© 2015.


  • Finite-size effects
  • Oscillatory component of level density
  • Quantum phase transitions
  • Regular/chaotic dynamics


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