H-NESSi: the hierarchical non-equilibrium systems simulation package

Blommel, Thomas (author), Kovačević, Jeremija (author), Kaye, Jason (author), Gull, Emanuel (author), Vučičević, Jakša (author), Golež, Denis (author)

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.

• Language: English
• Keywords: numerical simulations, nonequilibrium dynamics, quantum many-body problems, Keldysh formalism, Kadanoff-Baym equations, hierarchical low-rank compression
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2026
• Number of pages: 22 str.
• Numbering: Vol. 327, art. no. 110256
• PID: 20.500.12556/RUL-188097
• UDC: 53
• ISSN on article: 0010-4655
• DOI: 10.1016/j.cpc.2026.110256
• COBISS.SI-ID: 291495427
• Publication date in RUL: 18.09.2026

Record is a part of a journal

• Title: Computer physics communications
• Shortened title: Comput. phys. commun.
• Publisher: North-Holland
• ISSN: 0010-4655
• COBISS.SI-ID: 25260288

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: numerične simulacije, neravnovesna dinamika, kvantni večdelčni sistemi, Keldyshev formalizem, Kadanoff-Baymove enačbe