Hubbard模型的半经典近似与基于GPU技术的优化器相结合
Hubbard model on Semiclassical approximation in combination with an optimizer based on GPU technology
AI总结：
提出基于PyTorch与CUDA的SCA+ADAM半经典GPU方法，用于高效计算含长程关联的二维离子Hubbard模型，并与Hartree-Fock结果及多种物相性质对比。
摘要：
我们在图形处理器（GPU）上基于PyTorch和CUDA库，开发了一种将半经典近似方法与自适应矩估计优化器相结合的SCA + ADAM方法。该方法用于在合理的计算时间内评估具有长程空间关联的Hubbard模型的单粒子性质。该方法被应用于具有长程空间关联的二维正方晶格上的离子Hubbard模型。我们在中央处理器和GPU上评估了计算时间随晶格尺寸的变化。在此，我们还讨论了不存在离子势时Hubbard模型中的态密度和反铁磁（AF）序参量，并将结果与Hartree-Fock近似的结果进行了比较。最后，我们给出了离子Hubbard模型在电荷密度波、AF金属和AF绝缘体中的单粒子性质和序参量。
英文摘要：
We developed a semiclassical approximation method in combination with an adaptive moment estimation optimizer (SCA + ADAM) approach based on the PyTorch plus CUDA library on a the graphics processing unit (GPU). This method was employed to evaluate one-particle properties of the Hubbard model with long-range spatial correlations within an appropriate computing duration. The method was applied to the ionic Hubbard model on a two-dimensional square lattice with long-range spatial correlations. The computation time was evaluated as a function of the lattice size on the central processing unit and GPU. Herein, we also discuss the density of states and antiferromagnetic (AF) order parameter in the Hubbard model without the ionic potential and compare the results with those of the Hartree-Fock approximation. Finally, we present the one-particle properties and order parameter in charge density wave, AF metal and AF insulator of the ionic Hubbard model.
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