论文标题
哈伯德模型的密度基质嵌入理论的比较研究
Comparative study of the density matrix embedding theory for the Hubbard models
论文作者
论文摘要
我们研究了[G. Knizia和G. K.-L.陈，物理。莱特牧师。 109，186404（2012）]。该方法的核心是找到适当的一身电位，该潜力可以产生良好的试验函数，以将大规模的原始哈密顿量投射到具有少数基础的本地子系统上。预计哈密顿量的最终基态可以局部近似真正的基态状态。但是，缺乏各种原则使得很难判断潜力选择的质量。在这里，我们将重点放在纠缠范围（ES）作为判断标准上。对ES的准确评估可以确保相应的降低密度矩阵很好地再现了局部子系统上的所有物理量。我们将DMET应用于一维链，锯齿形链和三角形晶格上的Hubbard模型，并测试电势和成本函数的几种变体。事实证明，ES比能量和双人占用率更敏感，以探测DMET结果的质量。对称电势会从非相互作用极限继续延续的相位ES。 ES中的奇异性可以检测到Mott的过渡以及对称性的过渡。但是，强烈相互作用的参数区域中ES的细节在很大程度上取决于这些变体，这意味着当前的DMET算法允许众多变体不足以充分表征ES需要表征的特定阶段。
We examine the performance of the density matrix embedding theory (DMET) recently proposed in [G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. The core of this method is to find a proper one-body potential that generates a good trial wave function for projecting a large scale original Hamiltonian to a local subsystem with a small number of basis. The resultant ground state of the projected Hamiltonian can locally approximate the true ground state. However, the lack of the variational principle makes it difficult to judge the quality of the choice of the potential. Here we focus on the entanglement spectrum (ES) as a judging criterion; accurate evaluation of the ES guarantees that the corresponding reduced density matrix well reproduces all physical quantities on the local subsystem. We apply the DMET to the Hubbard model on the one-dimensional chain, zigzag chain, and triangular lattice and test several variants of potentials and cost functions. It turns out that ES serves as a more sensitive quantity than the energy and double occupancy to probe the quality of the DMET outcomes. A symmetric potential reproduces the ES of the phase that continues from a noninteracting limit. The Mott transition as well as symmetry-breaking transitions can be detected by the singularities in the ES. However, the details of the ES in the strongly interacting parameter region depends much on these variants, meaning that the present DMET algorithm allowing for numerous variant is insufficient to fully characterize the particular phases that require characterization by the ES.
