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Quantum phase transition and spectral statistics in Bose–Hubbard model

Author

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  • Saleki, Ziba
  • Jalili, Amir
  • Luo, Yan-An
  • Pan, Feng
  • Chen, Ai-Xi

Abstract

This study focuses on the quantum phase transition and the analysis of energy spectra with the objective of identifying chaotic and regular regimes within the Bose–Hubbard model, utilizing an algebraic theoretical framework. Additionally, we examine the variation of entanglement in the vicinity of quantum phase transitions induced by adjusting the pairing strength. To achieve this objective, we categorize the energy spectra to determine the chaoticity parameter (q) by analyzing the distribution of level spacing ratios. Our findings reveal that regions proximate to Rabi and Fock symmetries exhibit a Poisson-like distribution, whereas the vicinity of the shape-phase transition (Josephson regime) tends to display an intermediate distribution between regular and chaotic. Furthermore, within the scope of this study, we employ the Cramér–Rao lower bound to identify the minimum variance of the estimators.

Suggested Citation

  • Saleki, Ziba & Jalili, Amir & Luo, Yan-An & Pan, Feng & Chen, Ai-Xi, 2026. "Quantum phase transition and spectral statistics in Bose–Hubbard model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 683(C).
    • Handle: RePEc:eee:phsmap:v:683:y:2026:i:c:s0378437125008453
    DOI: 10.1016/j.physa.2025.131193
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