Lindbladian PT phase transitions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917178439106560 |
|---|---|
| author | Nakanishi, Yuma Sasamoto, Tomohiro |
| author_facet | Nakanishi, Yuma Sasamoto, Tomohiro |
| contents | A parity-time (PT) transition is a spectral transition characteristic of non-Hermitian generators; it typically occurs at an exceptional point, where multiple eigenvectors coalesce. The concept of a PT transition has been extended to Markovian open quantum systems, which are described by the GKSL equation. Interestingly, the PT transition in many-body Markovian open quantum systems, the so-called \textit{Lindbladian PT (L-PT) phase transition}, is closely related to two classes of exotic nonequilibrium many-body phenomena: \textit{continuous-time crystals} and \textit{non-reciprocal phase transitions}. In this review, we describe the recent advances in the study of L-PT phase transitions. First, we define PT symmetry in three distinct contexts: non-Hermitian systems, nonlinear dynamical systems, and Markovian open quantum systems, highlighting the interconnections between these frameworks. Second, we develop mean-field theories of L-PT phase transitions for collective-spin systems and for bipartite bosonic systems with particle-number conservation. Within these classes of models, we show that L-PT symmetry can induce a breaking of continuous time-translation symmetry down to a discrete one, leading to persistent periodic dynamics. We further demonstrate that the L-PT phase transition point is typically \textit{a critical exceptional point}, where multiple collective excitation modes with zero excitation spectrum coalesce. These findings establish an explicit connection to continuous-time crystals and non-reciprocal phase transitions. Third, going beyond the mean-field theory, we analyze statistical and quantum properties, such as purity and quantum entanglement indicators of time-independent steady states for several specific models with the L-PT symmetry. Finally, we discuss future research directions for L-PT phase transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lindbladian PT phase transitions Nakanishi, Yuma Sasamoto, Tomohiro Quantum Physics A parity-time (PT) transition is a spectral transition characteristic of non-Hermitian generators; it typically occurs at an exceptional point, where multiple eigenvectors coalesce. The concept of a PT transition has been extended to Markovian open quantum systems, which are described by the GKSL equation. Interestingly, the PT transition in many-body Markovian open quantum systems, the so-called \textit{Lindbladian PT (L-PT) phase transition}, is closely related to two classes of exotic nonequilibrium many-body phenomena: \textit{continuous-time crystals} and \textit{non-reciprocal phase transitions}. In this review, we describe the recent advances in the study of L-PT phase transitions. First, we define PT symmetry in three distinct contexts: non-Hermitian systems, nonlinear dynamical systems, and Markovian open quantum systems, highlighting the interconnections between these frameworks. Second, we develop mean-field theories of L-PT phase transitions for collective-spin systems and for bipartite bosonic systems with particle-number conservation. Within these classes of models, we show that L-PT symmetry can induce a breaking of continuous time-translation symmetry down to a discrete one, leading to persistent periodic dynamics. We further demonstrate that the L-PT phase transition point is typically \textit{a critical exceptional point}, where multiple collective excitation modes with zero excitation spectrum coalesce. These findings establish an explicit connection to continuous-time crystals and non-reciprocal phase transitions. Third, going beyond the mean-field theory, we analyze statistical and quantum properties, such as purity and quantum entanglement indicators of time-independent steady states for several specific models with the L-PT symmetry. Finally, we discuss future research directions for L-PT phase transitions. |
| title | Lindbladian PT phase transitions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.24981 |