NESSi: The Non-Equilibrium Systems Simulation package
Journal article, 2020

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green's functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green's functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green's functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green's functions. The library employs a discretization of the Kadanoff–Baym contour into time N points and a high-order implementation of integration routines. The total integrated error scales up to O(N−7), which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers. Program summary: Program Title: NESSi CPC Library link to program files: Licensing provisions: MPL v2.0 Programming language: C++, python External routines/libraries: cmake, eigen3, hdf5 (optional), mpi (optional), omp (optional) Nature of problem: Solves equations of motion of time-dependent Green's functions on the Kadanoff–Baym contour. Solution method: Higher-order solution methods of integral and integro-differential equations on the Kadanoff–Baym contour.

Keldysh formalism

Kadanoff–Baym equations

Numerical simulations

Nonequilibrium dynamics of quantum many-body problems


Michael Schüler

University of Fribourg

Stanford University

Denis Golež

Simons Foundation

University of Fribourg

Yuta Murakami

Tokyo Institute of Technology

University of Fribourg

Nikolaj Bittner

University of Fribourg

Andreas Herrmann

University of Fribourg

Hugo Strand

Chalmers, Physics, E-commons

Simons Foundation

Philipp Werner

University of Fribourg

Martin Eckstein

University of Erlangen-Nuremberg (FAU)

Computer Physics Communications

0010-4655 (ISSN)

Vol. 257 107484

Subject Categories

Computational Mathematics

Computer Science

Mathematical Analysis


C3SE (Chalmers Centre for Computational Science and Engineering)



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