Symmetry classification of many-body Lindbladians : tenfold way and beyond

Sá, Lucas (author), Ribeiro, Pedro (author), Prosen, Tomaž (author)

We perform a systematic symmetry classification of many-body Lindblad superoperators describing general (interacting) open quantum systems coupled to a Markovian environment. Our classification is based on the behavior of the many-body Lindbladian under antiunitary symmetries and unitary involutions. We find that Hermiticity preservation reduces the number of symmetry classes, while trace preservation and complete positivity do not, and that the set of admissible classes depends on the presence of additional unitary symmetries: in their absence or in symmetry sectors containing steady states, many-body Lindbladians belong to one of ten non-Hermitian symmetry classes; if however, there are additional symmetries and we consider non-steady-state sectors, they belong to a different set of 19 classes. In both cases, it does not include classes with Kramers degeneracy. Remarkably, our classification admits a straightforward generalization to the case of non-Markovian, and even non-trace-preserving, open quantum dynamics. While the abstract classification is completely general, we then apply it to general (long-range, interacting, spatially inhomogeneous) spin-1/2 chains. We explicitly build examples in all ten classes of Lindbladians in steady-state sectors, describing standard physical processes such as dephasing, spin injection and absorption, and incoherent hopping, thus illustrating the relevance of our classification for practical physics applications. Finally, we show that the examples in each class display unique random-matrix correlations. To fully resolve all symmetries, we employ the combined analysis of bulk complex spacing ratios and the overlap of eigenvector pairs related by symmetry operations. We further find that statistics of levels constrained onto the real and imaginary axes or close to the origin are not universal due to spontaneous breaking of Lindbladian PT symmetry.

• Language: English
• Keywords: condensed matter physics, quantum statistical mechanics, quantum physics, statistical physics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 22 str.
• Numbering: Vol. 13, iss. 3, art. 031019
• PID: 20.500.12556/RUL-155461
• UDC: 536.93
• ISSN on article: 2160-3308
• DOI: 10.1103/PhysRevX.13.031019
• COBISS.SI-ID: 191230723
• Publication date in RUL: 03.04.2024

SÁ, Lucas, RIBEIRO, Pedro and PROSEN, Tomaž, 2023, Symmetry classification of many-body Lindbladians : tenfold way and beyond. Physical review [online]. 2023. Vol. 13, no. 3,  031019. [Accessed 23 June 2025]. DOI 10.1103/PhysRevX.13.031019. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=155461

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., X
• Publisher: American Physical Society
• ISSN: 2160-3308
• COBISS.SI-ID: 19686152

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: fizika kondenzirane snovi, kvantna statistična mehanika