20.500.12556/RUL-155461 Symmetry classification of many-body Lindbladians tenfold way and beyond 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. condensed matter physics quantum statistical mechanics quantum physics statistical physics fizika kondenzirane snovi kvantna statistična mehanika true false true Angleški jezik Slovenski jezik Članek v reviji 2024-04-03 11:26:31 2024-04-03 11:26:32 2024-12-11 11:05:46 0000-00-00 00:00:00 2023 0 0 22 str. iss. 3, art. 031019 Vol. 13 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 536.93 2160-3308 10.1103/PhysRevX.13.031019 191230723 PhysRevX.13.031019.pdf PhysRevX.13.031019.pdf 1 2D3C115B1327082F149AE3D50BA05DA1 bc6abb6be2e0d288e390d60793aad8db368186237747aefc0a7bed0a854c773f 843eb8d1-f19c-11ee-853b-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=182359 https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.031019 0 8d6d45d1-f19c-11ee-853b-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=182360 Fakulteta za matematiko in fiziko 0 0 0