NESSi: The Non-Equilibrium Systems Simulation package

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.

关联多粒子系统（correlated many-particle systems）的非平衡动力学（nonequilibrium dynamics），与分子系统及固体的泵浦-探测实验、输运性质与弛豫过程的理论研究密切相关。非平衡格林函数（Nonequilibrium Green’s functions）是研究非平衡量子多粒子系统相互作用效应、提取可用于实验诠释的物理相关信息的有力工具。我们推出了开源软件包NESSi（非平衡系统模拟软件包，The Non-Equilibrium Systems Simulation package），该工具支持基于卡达诺夫-贝姆轮廓（Kadanoff-Baym contour）上的格林函数开展多体动力学模拟。NESSi包含核心库libcntr，其实现了针对此类非平衡格林函数的基础运算、费曼图（Feynman diagrams）构建，以及涉及闭合轮廓格林函数的积分与积分微分方程求解功能。该库将卡达诺夫-贝姆轮廓离散为N个时间节点，并集成了高阶积分运算程序。总积分误差可缩放至O(N⁻⁷)，这一特性尤为关键，因为数值计算开销随模拟时长至少呈三次方增长。通过在倒易空间（reciprocal space）上实现分布式内存并行化，可完成晶格系统的大规模模拟。我们提供了一系列示例程序，覆盖从简单二能级系统动力学，到当代凝聚态物理相关问题的各类场景，包括哈伯德团簇（Hubbard clusters）以及哈伯德或霍尔斯坦晶格模型（Hubbard or Holstein lattice models）。libcntr库同时也是后续一款基于强耦合微扰杂质求解器（strong-coupling perturbative impurity solvers）的非平衡动力学平均场理论（nonequilibrium dynamical mean-field theory）计算软件包的核心基础。