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  • Open Access

Detailed study on phase transitions in the dissipative anisotropic Dicke model

Pragna Das1,2,* and Saptarshi Saha3,4,†

  • *Contact author: pragnad90@gmail.com
  • †Contact author: s.saha@tu-berlin.de
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Phys. Rev. A 114, 013726 – Published 31 July, 2026

DOI: https://doi.org/10.1103/47gn-l4dm

Abstract

We present a comprehensive study of different phase transitions in the Dicke model incorporating both anisotropy and dissipation. We begin with a concise review of the quantum phase transition in this setting, highlighting how these two parameters shift the critical point. We then perform a detailed investigation of the transition from ergodic to nonergodic phases by analyzing the eigenvalue and eigenvector properties of the Liouvillian with the aid of scaling of the Liouvillian gap and the average participation ratio. Our results show that the eigenvector properties of the Liouvillian are consistent with its spectral characteristics, leading to a phase diagram that has similarities to the closed counterpart. In particular, the steady-state properties are associated with the quantum phase transition, whereas the decaying modes retain signatures of the ergodic to nonergodic transition. Furthermore, we demonstrate that the Liouvillian gap exhibits distinct scaling behaviors in these two phases. Finally, we extend our study to the driven case by applying a Thue-Morse quasiperiodic drive. In this case, we find that bosonic dissipation plays a crucial role in stabilizing the prethermal plateau, offering an effective mechanism to halt the heating effect arising from the quasiperiodic drive.

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Phys. Rev. A 114, 013726– Published 31 July, 2026
  • Received 22 January 2026
  • Accepted 8 July 2026
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