WannierNLQG：一个用于从Wannier紧束缚模型计算非线性光学响应和量子几何的Julia软件包
WannierNLQG: A Julia package for nonlinear optical responses and quantum geometry from Wannier tight-binding models
- Center for Quantum Matter, School of Physics, Zhejiang University（浙江大学物理学院量子物质中心）
- Department of Physics, City University of Hong Kong（香港城市大学物理系）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文介绍WannierNLQG，一个Julia软件包，用于从Wannier紧束缚模型计算非线性光学响应和量子几何量，支持任意阶微扰、简并处理及对称性工作流，可应用于真实多带材料的第一性原理研究。
中文摘要 AI 辅助
非线性光学响应和量子几何是现代凝聚态物理学的核心，并且两者密切相关。我们介绍了WannierNLQG，一个可扩展的Julia框架，用于从Wannier紧束缚模型计算非线性光学响应和量子几何量。其规范一致、简并感知的架构可容纳任意阶的微扰响应和额外的量子几何量。当前版本评估普通、自旋和光子拖曳注入及位移电流，作为布里渊区积分以及在k切片上进行。对于位移电流，统一接口提供了四种互补公式：常规方法、投影子迹、广义Wilson环和有限动量几何环，其中后三种明确适用于简并子空间。该框架还提供k分辨的Berry曲率、量子度量、它们的多极矩以及额外的量子几何和混合动量-自旋量。实验对称性工作流还支持对称性适配的Wannier构造、紧束缚模型和实空间算子的对称化，以及将空间均匀响应积分约化为不可约k点轨道和不变张量分量。文档涵盖了公式约定、TaskConfig接口和可审计的输出格式，并以GeS和双层MoS2案例研究说明了方法比较、简并处理、量子几何分析和光子拖曳响应。这些能力共同使得对现实多带材料进行非线性响应和量子几何的第一性原理计算成为可能，将量子几何与用于光电、自旋电子和光伏应用的定量材料建模联系起来。
英文摘要
Nonlinear optical responses and quantum geometry are central to modern condensed matter physics and are deeply intertwined. We introduce WannierNLQG, an extensible Julia framework for computing nonlinear optical responses and quantum geometric quantities from Wannier tight-binding models. Its gauge-consistent, degeneracy-aware architecture accommodates perturbative responses at arbitrary order and additional quantum geometric quantities. The current release evaluates ordinary, spin, and photon-drag injection and shift currents, as Brillouin-zone integrals and on k slices. For shift current, a unified interface exposes four complementary formulations: the conventional method, projector trace, generalized Wilson loop, and a finite-momentum geometric loop, with the last three explicitly accommodating degenerate subspaces. The framework also provides k-resolved Berry curvature, quantum metric, their multipoles, and additional quantum geometric and mixed momentum-spin quantities. Experimental symmetry workflows additionally support symmetry-adapted Wannier construction, symmetrization of tight-binding models and real-space operators, and reduction of spatially uniform response integrals to irreducible k-point orbits and invariant tensor components. The documentation covers formula conventions, the TaskConfig interface, and auditable output formats, with GeS and bilayer MoS2 case studies illustrating method comparison, degeneracy handling, quantum geometric analysis, and photon-drag responses. Together, these capabilities enable first-principles calculations of nonlinear response and quantum geometry in realistic multiband materials, connecting quantum geometry with quantitative materials modeling for optoelectronic, spintronic, and photovoltaic applications.
