AI 中文总结
将海森堡自旋哈密顿量有限温度兰索斯方法的GPU实现，从总磁化对称性扩展到包括非阿贝尔点群和空间群的全置换对称性。对高度对称簇，置换群多维不可约表示可减块维度，提供无矩阵形式，演示运行并给出代码信息。
AI 中文摘要
我们将最近针对海森堡自旋哈密顿量的有限温度兰索斯方法（FTLM）的GPU实现进行扩展，从仅使用总磁化对称性扩展到包括非阿贝尔点群和空间群的全置换对称性。对于高度对称的簇，置换群的多维不可约表示能进一步大幅减小块维度。我们提供了一种无矩阵形式来利用此类对称性，该实现同样适用于阿贝尔群并保留GPU加速优势。文中给出了在单个NVIDIA B200加速器上对十二面体上s = 3/2海森堡反铁磁体及5x8格点的s = 1/2正方形晶格的生产运行演示，并给出了代码的相关信息。
英文摘要
We extend a recent GPU implementation of the finite-temperature Lanczos method (FTLM) for Heisenberg spin Hamiltonians, which uses only total-magnetization symmetry, to the full permutation symmetry, including non-Abelian point and space groups. For highly symmetric clusters such as icosahedral polyhedra, the multidimensional irreducible representations (irreps) of the permutation group reduce the block dimensions substantially further than any Abelian subgroup. Here, we provide a matrix-free formalism (avoiding explicit storage of the projected Hamiltonian) for using such symmetries. The implementation applies equally to Abelian groups, retaining the advantages of GPU acceleration. Several cluster topologies are built in; beyond these, symmetry groups can be supplied as site-permutation generators, with irrep matrices computed automatically, so that user-defined clusters run without any code changes. We demonstrate the approach in production runs on a single NVIDIA B200 accelerator for the s=3/2 Heisenberg antiferromagnet on the dodecahedron (Hilbert-space dimension 4^20 ~ 1.1x10^12) and for the s=1/2 square lattice of 5x8 sites (M=0 dimension 1.4x10^11). With R=24 random vectors per symmetry block and 60 Lanczos steps, the dodecahedron campaign (with the largest iterated symmetry block having a dimension of 3.6x10^9) requires about 50 GPU-hours. The code is openly available under the Apache-2.0 license at https://github.com/ghasdeke/ftlm-pg-gpu, archived at DOI: 10.5281/zenodo.21445872.
Comments28 pages, 6 figures
