NESSi: The Non-Equilibrium Systems Simulation package

TL;DR

The paper introduces NESSi, an open-source software package for simulating nonequilibrium many-particle quantum systems using Green's functions, enabling large-scale, high-accuracy dynamics simulations.

Contribution

It presents a new software library, libcntr, with high-order integration and parallelization capabilities for nonequilibrium Green's function calculations, facilitating advanced quantum dynamics studies.

Findings

Achieves up to O(N^{-7}) error scaling in simulations.

Enables large-scale lattice system simulations with distributed-memory parallelization.

Provides example programs for various condensed matter physics models.

Abstract

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 $\mathcal{O}(N^{-7})$, 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.