关于密度矩阵嵌入理论的纯态$v$ -可表示性
On the pure state $v$-representability of density matrix embedding theory
摘要：
密度矩阵嵌入理论（DMET）在形式上要求由高层次理论和低层次理论得到的密度矩阵块匹配，但这在实际计算中有时无法实现。在这种情况下，低能级理论的全局带隙消失，这可能需要额外的数值考虑。我们发现，违反精确匹配条件和消失的低级别的差距有关的假设，即高级别的密度矩阵块是非相互作用的纯态$v$ -representable（NI-PS-V），它假定低级别的密度矩阵构造遵循Aufbau原则。为了放宽NI-PS-V条件，我们发展了一种增广拉格朗日方法来匹配密度矩阵块，而不涉及Aufbau原理。2D Hubbard和氢模型系统的数值结果表明，在一些具有挑战性的情况下，Aufbau原理的放松直接导致密度矩阵块的精确匹配，这也产生了更高的精度。
英文摘要：
Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are non-interacting pure-state $v$-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. In order to relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for 2D Hubbard and hydrogen model systems indicate that in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.
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