TBPLaS: A tight-binding package for large-scale simulation

TBPLaS is an open-source software package for the accurate simulation of physical systems with arbitrary geometry and dimensionality utilizing the tight-binding (TB) theory. It has an intuitive object-oriented Python application interface (API) and Cython/Fortran extensions for the performance-critical parts, ensuring both flexibility and efficiency. Under the hood, numerical calculations are mainly performed by both exact diagonalization and the tight-binding propagation method (TBPM) without diagonalization. Especially, the TBPM is based on the numerical solution of the time-dependent Schrödinger equation, achieving linear scaling with system size in both memory and CPU costs. Consequently, TBPLaS provides a numerically cheap approach to calculate the electronic, optical, plasmon and transport properties of large tight-binding models with billions of atomic orbitals. Current capabilities of TBPLaS include the calculations of band structure, density of states, local density of states, quasi-eigenstates, optical conductivity, electrical conductivity, Hall conductivity, polarization function, dielectric function, plasmon dispersion, carrier mobility and velocity, localization length and free path, topological invariant, wave-packet propagation, etc. All the properties can be obtained with only a few lines of code. Other algorithms involving tight-binding Hamiltonians can be implemented easily due to the extensible and modular nature of the code. In this paper, we discuss the theoretical framework, implementation details and common workflow of TBPLaS, and give a few demonstrations of its applications.

TBPLaS是一款开源软件包，可借助紧束缚（tight-binding, TB）理论，对任意几何构型与维度的物理系统开展精准模拟。其配备直观的面向对象Python应用程序接口（API），并针对性能敏感模块集成了Cython与Fortran扩展，在保证灵活性的同时兼顾了计算效率。底层数值计算主要同时采用严格对角化与无需对角化的紧束缚传播方法（tight-binding propagation method, TBPM）。尤为关键的是，TBPM基于含时薛定谔方程的数值解法，可在内存与CPU开销上实现随系统规模线性缩放的计算复杂度。据此，TBPLaS可为包含数十亿原子轨道的大型紧束缚模型，提供一种计算成本低廉的方案，用于计算其电子、光学、等离激元与输运性质。目前TBPLaS支持的计算功能涵盖能带结构、态密度、局域态密度、准本征态、光导率、电导率、霍尔电导率、极化函数、介电函数、等离激元色散、载流子迁移率与速度、局域化长度与自由程、拓扑不变量、波包传播等。仅需编写数行代码即可完成上述所有性质的计算。得益于代码的模块化与可扩展特性，其他涉及紧束缚哈密顿量的算法均可轻松集成。本文将详述TBPLaS的理论框架、实现细节与通用工作流程，并展示若干应用示例。