TBPLaS 2.0: A tight-binding package for large-scale simulation

The common exact diagonalization-based techniques to solving tight-binding models suffer from O(N^2) and O(N^3) scaling with respect to model size in memory and CPU time, hindering their applications in large tight-binding models. On the contrary, the tight-binding propagation method (TBPM) can achieve linear scaling in both memory and CPU time, and is capable of handling large tight-binding models with billions of orbitals. In this paper, we introduce version 2.0 of TBPLaS, a package for large-scale simulation based on TBPM [1]. This new version brings significant improvements with many new features. Existing Python/Cython modeling tools have been thoroughly optimized, and a compatible C++ implementation of the modeling tools is now available, offering efficiency enhancement of several orders. The solvers have been rewritten in C++ from scratch, with the efficiency enhanced by several times or even by an order of magnitude. The workflow of utilizing solvers has also been unified into a more comprehensive and consistent manner. New features include spin texture, Berry curvature and Chern number calculation, partial diagonalization for specific eigenvalues and eigenstates, analytical Hamiltonian, and GPU computing support. The documentation and tutorials have also been updated to the new version. In this paper, we discuss the revisions with respect to version 1.3 and demonstrate the new features. Benchmarks on modeling tools and solvers are also provided.

当前用于求解紧束缚模型（tight-binding model）的主流基于严格对角化的技术，在内存与CPU时间开销上均呈现与模型规模相关的O(N²)和O(N³)复杂度增长，极大限制了其在大规模紧束缚模型中的应用。与之相对，紧束缚传播方法（tight-binding propagation method，TBPM）可在内存与CPU时间开销上实现线性复杂度缩放，能够处理包含数十亿轨道的大规模紧束缚模型。本文介绍了基于TBPM的大规模模拟工具包TBPLaS的2.0版本[1]。该新版本实现了多项显著改进，新增了诸多功能特性。原有的Python/Cython建模工具已得到全面优化，同时新增了与之兼容的C++实现版本，可将计算效率提升数个量级。求解器已完全基于C++从头重构，计算效率提升数倍乃至一个量级。求解器的使用流程也已统一为更全面且一致的操作范式。新增功能包括自旋纹理、贝里曲率（Berry curvature）与陈数（Chern number）计算、针对特定本征值与本征态的部分对角化、解析哈密顿量以及GPU计算支持。配套文档与教程也已同步更新至该新版本。本文详细讨论了相较于1.3版本的更新内容，并对新增功能进行了演示，同时提供了针对建模工具与求解器的性能基准测试结果。