Quantum spin solver near saturation: QS3

We develop a program package named QS3 based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models on spatially uniform/non-uniform lattices near fully polarized states, which can be mapped to dilute hardcore Bose systems. All calculations in QS3, including eigenvalue problems, expectation values for one/two-point spin operators, and static/dynamical spin structure factors, are performed in the symmetry-adapted bases specified by the number N↓ of down spins and the wave number k associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS3 can support large-scale quantum systems containing more than 1000 sites with dilute N↓. We show the benchmark results of QS3 for the low-energy excitation dispersion of the isotropic Heisenberg model on the 10 x 10 x 10 cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the 10 x 10 square lattice, and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP). Theoretical backgrounds and the user interface of QS3 are also described.我们开发了一款基于（厚重启）兰佐斯（Lanczos）方法的程序包QS3，用于分析空间均匀/非均匀晶格上、接近全极化态的自旋1/2 XXZ型量子自旋模型——这类模型可被映射为稀释硬核玻色系统。QS3中的所有计算，涵盖本征值问题、一二点自旋算符的期望值以及静态与动态自旋结构因子的求解，均采用由下自旋数N↓与平移对称性关联的波矢k所确定的对称适配基进行，且无需借助比特表示来指定自旋组态。得益于上述处理策略，QS3可支持位点数量超过1000且下自旋数处于稀释状态的大规模量子系统。我们展示了QS3的三项基准测试结果：10×10×10立方晶格上各向同性海森堡模型的低能激发色散、10×10方格晶格上各向同性海森堡模型的静态与动态自旋结构因子，以及部署于固体物理研究所（ISSP）、搭载AMD Epyc 7702处理器的名为Ohtaka的超级计算机上的OpenMP并行效率。本文同时阐述了QS3的理论背景与用户界面。