论文标题
Hohenberg-Kohn定理对通用量子系统的可扩展性
Extensibility of Hohenberg-Kohn Theorem to general quantum systems
论文作者
论文摘要
Hohenberg-Kohn（HK）定理是现代电子结构计算的基石。对于相互作用的电子，鉴于哈密顿量的内部部分（$ \ hat h_ {int} $）包含电子的动能和库洛姆的相互作用，具有固定形式，该定理指出，当电子将受到外部静电场的影响时，地面密度可以完全确定地面密度，从而完全确定该场，从而完全确定完整的Hamililtonian。对于通用量子系统，以$ \ hat h_ {hk} \ {g_i \} = \ h_h_ {int}+sum_i g_i \ hat o_i $的始终将这些术语与固定的系数分组为$ \ h_的超级{一组Hermitian操作员$ \ {\ hat o_i \} $。我们询问是否可以扩展香港定理，以便将$ \ {\ hat o_i \} $的地面期望值原理用作确定系统所有属性的基本变量。我们表明，可以通过介绍根据$ \ {\ hat o_i \} $运算符定义的广义密度相关矩阵（GDCM）的概念来解决这个问题。 GDCM的可逆性代表了数学上严格且实际上有用的标准，用于扩展HK定理的有效。我们将此标准应用于几个代表性系统，包括量子iSing二聚体，无挫败感系统，具有固定层次间过渡幅度和可调水平能量的N级量子系统，以及具有不均匀的室内相互作用的费尔米金哈伯德链。我们建议对于有限大小的系统，在一个$ \ {g_i \} $配置下找到可逆的GDCM通常足以在整个参数空间中建立HK定理的通用可扩展性。
Hohenberg-Kohn (HK) theorem is a cornerstone of modern electronic structure calculations. For interacting electrons, given that the internal part of the Hamiltonian ($\hat H_{int}$), containing the kinetic energy and Couloumb interaction of electrons, has a fixed form, the theorem states that when the electrons are subject to an external electrostatic field, the ground-state density can inversely determine the field, and thus the full Hamiltonian completely. For a general quantum system, a HK-type Hamiltonian in the form of $\hat H_{hk}\{g_i\}=\hat H_{int}+\sum_i g_i \hat O_i$ can always be defined, by grouping those terms with fixed or preknown coefficients into $\hat H_{int}$, and factorizing the remaining as superposition of a set of Hermitian operators $\{\hat O_i\}$. We ask whether the HK theorem can be extended, so that the ground-state expectation values of $\{\hat O_i\}$ as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. We show that the question can be addressed by introducing the concept of generalized density correlation matrix (GDCM) defined with respect to the $\{\hat O_i\}$ operators. The invertibility of the GDCM represents a mathematically rigorous and practically useful criterion for the extension of HK theorem to be valid. We apply this criterion to several representative systems, including the quantum Ising dimer, the frustration-free systems, N-level quantum systems with fixed inter-level transition amplitude and tunable level energies, and a fermionic Hubbard chain with inhomogeneous on-site interactions. We suggest that for a finite-size system, finding an invertible GDCM under one single $\{g_i\}$ configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space.
