结合Mott物理、自旋相关现象和空间不均匀性的无限Hubbard链基态能量的简单参数化
Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
摘要：
给出了一维排斥哈伯德模型的基态能量的简单解析参数化表达式。的电荷依赖性的能量是参数化的使用从Bethe-Anglands提取的精确结果。所得到的参数化被证明是在更好的协议与高精度的数据从完全数值解的Bethe-Angloman方程比以前的表达式[利马等人，物理修订信函90，146402（2003）]。与这些早期的建议，本参数化正确地预测一个积极的莫特间隙在任何U>0的一半填充。该结构扩展到自旋相关的现象参数化的磁化依赖的基态能量使用进一步的精确结果和数值基准。最后，为空间均匀模型开发的参数化通过简单的局部密度型近似扩展到空间非均匀模型，例如，在存在杂质、外部场或俘获电势的情况下。结果表明，在良好的协议与独立的多体计算，在一小部分的计算成本。
英文摘要：
Simple analytical parametrizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge-dependence of the energy is parametrized using exact results extracted from the Bethe-Ansatz. The resulting parametrization is shown to be in better agreement with highly precise data obtained from fully numerical solution of the Bethe-Ansatz equations than previous expressions [Lima et al., Phys. Rev. Lett. 90, 146402 (2003)]. Unlike these earlier proposals, the present parametrization correctly predicts a positive Mott gap at half filling for any U>0. The construction is extended to spin-dependent phenomena by parametrizing the magnetization-dependence of the ground-state energy using further exact results and numerical benchmarking. Lastly, the parametrizations developed for the spatially uniform model are extended by means of a simple local-density-type approximation to spatially inhomogeneous models, e.g., in the presence of impurities, external fields or trapping potentials. Results are shown to be in excellent agreement with independent many-body calculations, at a fraction of the computational cost.
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