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

Abstract

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.

Keywords

fizika kondenzirane snovi;kvantna statistična mehanika;condensed matter physics;quantum statistical mechanics;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 536.93
COBISS: 191230723 Link will open in a new window
ISSN: 2160-3308
Views: 7
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Other data

Secondary language: Slovenian
Secondary keywords: fizika kondenzirane snovi;kvantna statistična mehanika;
Type (COBISS): Article
Pages: str. 031019-1-031019-22
Volume: ǂVol. ǂ13
Issue: ǂiss. ǂ3
Chronology: 2023
DOI: 10.1103/PhysRevX.13.031019
ID: 23332603