We present a hybrid numerical approach to simulate quantum many-body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art high-performance computing infrastructures. We demonstrate that for the two-dimensional spinless fermion model and for the Hubbard model on torus geometry, altogether several orders of magnitude in computational time can be saved by performing calculations on an optimized basis and by utilizing hybrid CPU-multiGPU parallelization. At least an order of magnitude reduction in computational complexity results from mode optimization, while a further order of reduction in wall time is achieved by massive parallelization. Our results are measured directly in the number of floating point operations and seconds. A detailed scaling analysis of the obtained performance as a function of matrix ranks and as a function of system size up to $12\times 12$ lattice topology is discussed. Our CPU-multiGPU model also tremendously accelerates the calculation of the one- and two-particle reduced density matrices, which can be used to construct various order parameters and trace quantum phase transitions with high fidelity.

中文翻译：

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通过模式优化混合 CPU-GPU 密度矩阵重整化群方法的二维量子晶格模型

我们提出了一种混合数值方法，通过最先进的高性能计算基础设施上的密度矩阵重整化群方法的非阿贝尔从头算版本来模拟二维空间维度量子晶格模型上的量子多体问题。我们证明，对于二维无旋费米子模型和环面几何上的 Hubbard 模型，通过在优化的基础上执行计算并利用混合 CPU-多 GPU 并行化，可以节省几个数量级的计算时间。模式优化至少可以使计算复杂度降低一个数量级，而通过大规模并行化可以进一步减少挂壁时间。我们的结果直接以浮点运算次数和秒数来衡量。对所获得的性能进行详细的缩放分析，作为矩阵等级的函数和系统大小的函数$12\times 12$讨论了晶格拓扑。我们的CPU-多GPU模型还极大地加速了一粒子和二粒子降低密度矩阵的计算，该矩阵可用于构造各种阶参数并高保真度地追踪量子相变。