费米子格点系统密度-势映射的唯一性
Uniqueness of density-to-potential mapping for fermionic lattice systems
摘要：
我们证明了，对于一个费米子晶格系统，基态粒子密度唯一地决定了外部的潜力，除了网站对应的波函数的节点，和极限情况下，泡利不相容原理完全决定了所有网站的占领。我们的基本发现完成了，对于这类一般的系统，基态，它们的密度，和在霍恩伯格-科恩定理的基础上的外部潜力之间的一一对应。此外，我们还证明了从波函数到势函数的映射不仅对基态是唯一的，而且对激发态也是唯一的。为了说明我们的研究结果，我们开发了一个实用的反演方案，以确定从一个给定的密度的外部潜力。我们的结果适用于一般类型的晶格模型，其中包括哈伯德模型。
英文摘要：
We demonstrate that, for a fermionic lattice system, the ground-state particle density uniquely determines the external potential except for the sites corresponding to nodes of the wave function, and the limiting case where the Pauli exclusion principle completely determines the occupation of all sites. Our fundamental finding completes, for this general class of systems, the one-to-one correspondence between ground states, their densities, and the external potential at the base of the Hohenberg-Kohn theorem. Moreover we demonstrate that the mapping from wave function to potential is unique not just for the ground state, but also for excited states. To illustrate our findings, we develop a practical inversion scheme to determine the external potential from a given density. Our results hold for a general class of lattice models, which includes the Hubbard model.
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