20.500.12556/RUL-188097 H-NESSi: the hierarchical non-equilibrium systems simulation package We present H-NESSi (The Hierarchical Non-Equilibrium Systems Simulation package), an open-source software package for solving the Kadanoff-Baym equations (KBE) of nonequilibrium Green’s function (NEGF) theory using hierarchical low-rank compression techniques. The simulation of correlated quantum systems out of equilibrium is severely limited by the cubic scaling in propagation time and quadratic memory growth associated with conventional two-time formulations. H-NESSi overcomes these limitations by combining high-order time-stepping schemes with hierarchical off-diagonal low-rank (HODLR) representations of the retarded and lesser Green’s functions, enabling controllable accuracy at substantially reduced computational cost and memory usage. Imaginary-time quantities are efficiently represented using the discrete Lehmann representation (DLR), enabling compact and accurate treatment of thermal initial states. The implementation supports multiorbital systems, adaptive singular value truncation, and both shared-memory (OpenMP) and distributed-memory (MPI) parallelization strategies suitable for large-scale lattice calculations. The workflow closely mirrors established NEGF frameworks while introducing compression transparently into the propagation procedure. Benchmark applications to driven superconductors within dynamical mean-field theory and to the two-dimensional Hubbard model demonstrate favorable scaling compared to conventional implementations, with asymptotic time complexity significantly below the cubic scaling of uncompressed approaches. H-NESSi thus enables long-time and large-system nonequilibrium simulations of correlated quantum materials, which were previously computationally prohibitive. numerical simulations nonequilibrium dynamics quantum many-body problems Keldysh formalism Kadanoff-Baym equations hierarchical low-rank compression numerične simulacije neravnovesna dinamika kvantni večdelčni sistemi Keldyshev formalizem Kadanoff-Baymove enačbe true false true Angleški jezik Slovenski jezik Članek v reviji 2026-09-18 09:04:41 2026-09-18 09:04:43 2026-09-19 04:30:07 0000-00-00 00:00:00 2026 0 0 22 str. art. no. 110256 Vol. 327 Oct. 2026 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2028-06-19 53 0010-4655 10.1016/j.cpc.2026.110256 291495427 https://www.sciencedirect.com/science/article/pii/S0010465526002389 1 2f0bd609-b32f-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=248097 main.pdf main.pdf 1 EE106928113E4400AF0629FC88A4B0C7 64053d1aa652b65ec2dbf6f4cae71241b4a5ff7f42f8b9666e9fc0ef9338864d 8c10a39b-b32f-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=248098 Fakulteta za matematiko in fiziko 0 0 0