We examine the performance of the density matrix embedding theory (DMET) recently proposed in Knizia and 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 bases. 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.

中文翻译：

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Hubbard模型密度矩阵嵌入理论的比较研究

我们研究了最近在Knizia和Chan [ Phys。牧师 109，186404（2012）]。该方法的核心是找到合适的单体势能，该势能产生良好的试验波函数，以将大规模的原始哈密顿量投影到具有少量碱基的局部子系统。投影哈密顿量的合成基态可以局部近似于真实基态。但是，由于缺乏变分原理，因此很难判断电位选择的质量。在这里，我们将重点放在纠缠谱（ES）作为判断标准上。ES的准确评估可确保相应的密度降低的矩阵很好地再现了本地子系统上的所有物理量。我们将DMET应用于一维链，锯齿形链和三角晶格的Hubbard模型，并测试电势和成本函数的几种变体。事实证明，ES比能量和双重占用更为敏感，可以用来探测DMET结果的质量。对称电势再现了从非相互作用极限开始的相位的ES。可以通过ES中的奇异性来检测Mott过渡以及对称断开过渡。但是，在强烈相互作用的参数区域中ES的细节很大程度上取决于这些变量，这意味着允许多种变量的本DMET算法不足以完全表征需要ES表征的特定相位。可以通过ES中的奇异点来检测Mott过渡以及对称断开过渡。但是，在强烈相互作用的参数区域中ES的细节很大程度上取决于这些变量，这意味着允许多种变量的本DMET算法不足以完全表征需要ES表征的特定相位。可以通过ES中的奇异点来检测Mott过渡以及对称断开过渡。然而，在强烈相互作用的参数区域中ES的细节很大程度上取决于这些变量，这意味着允许多种变量的本DMET算法不足以完全表征需要ES表征的特定相位。