Householder变换密度矩阵泛函嵌入理论
Householder transformed density matrix functional embedding theory
摘要：
利用么正Householder变换，重新研究了基于单电子约化密度矩阵的量子嵌入.在非相互作用的情况下，虽然精确和等价于（但形式上比）密度矩阵嵌入理论（DMET），所得到的Householder变换的密度矩阵功能嵌入理论（Ht-DMFET）保留，通过建设，单粒子特性的浴时，电子相关的介绍。在Ht-DMFET中，投影的“杂质+浴”簇的哈密顿量（从中可以提取相互作用晶格的近似局部性质）变成密度矩阵的显式泛函。在单杂质DMET的精神，我们认为在这项工作中，一个封闭的（两个电子）集群从全尺寸的非相互作用的密度矩阵。当（Householder变换）的相互作用的浴网站上考虑到，每站点的能量得到的半满一维哈伯德晶格匹配几乎完美的确切Bethe Anastrous结果在所有相关制度。在强相关的制度，结果恶化远离半填充。这可能与（两个站点）集群中的电子数波动有关，这在Ht-DMFET和常规DMET中都没有描述。正如预期的那样，当增加嵌入的杂质的数量时，每个位点的能量显著提高。与密度/密度矩阵泛函理论的形式联系已经简要讨论过，应该进一步探讨。目前正在朝这个方向开展工作。
英文摘要：
Quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected "impurity+bath" cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the (Householder transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are not described neither in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
