电子结构计算中指数壁的处理
Dealing with the exponential wall in electronic structure calculations
摘要：
密度泛函理论的一种替代方法是基于波函数的固体电子结构计算。为了执行它们，必须解决指数壁（EW）问题。这是由于随着电子数N的增加，组态的数目呈指数增加而引起的。有不同的路线可以遵循。一种是在具有累积量度量的Liouville空间中而不是在Hilbert空间中用向量来刻画多电子波函数。这消除了EW问题。另一种方法是通过嵌入在{ \it浴}中的{ \it杂质}或{ \it片段}来模拟固体，所述{ \it浴}以比前者低得多的水平处理。这是密度矩阵嵌入理论（DMET）或密度嵌入理论（DET）中的情况。后者是密切相关的施密特分解的系统和相关的纠缠的测定。我们在这里展示这两种方法之间的联系。事实证明，DMET（或DET）具有与先前使用的Local Analog相同的活动空间，基于投影和分区方法。然而，在这两种情况下，电子战问题的解决方式不同。通过研究一个$H_{10}$环，用增量法分析了这些差异。
英文摘要：
An alternative to Density Functional Theory are wavefunction based electronic structure calculations for solids. In order to perform them the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated at a much lower level than the former. This is the case in Density Matrix Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a $H_{10}$ ring these differences are analyzed with the help of the method of increments.
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