论文标题
得出激发态的密度 - 矩阵功能
Deriving density-matrix functionals for excited states
论文作者
论文摘要
我们启动最近提出的$ \ boldsymbol {w} $ - 集合单粒子降低密度矩阵功能理论（$ \ boldsymbol {w} $ - rdmft），通过得出第一个功能近似值并说明如何在实践中计算激发能量。为此，我们首先研究了对称Hubbard二聚体，该二聚体构成了Hubbard模型的基础，为此我们执行了Levy-lieb受约束的搜索。其次，由于$ \ boldsymbol {w} $ - RDMFT的特殊适用性用于描述Bose-Einstein冷凝物，我们在Bogoliubov制度中演示了三种概念上不同的方法，用于在均匀的Bose Gas中推导通用功能，以进行任意对的相互作用。值得注意的是，在这两个系统中，该功能的梯度都可以在功能域的边界上排斥，从而将最近发现的Bose-Einstein凝结力扩展到激发态。我们的发现强调了费尔米金和玻色粒混合状态的普遍排除原则以及功能理论中普遍性的诅咒的物理相关性。
We initiate the recently proposed $\boldsymbol{w}$-ensemble one-particle reduced density matrix functional theory ($\boldsymbol{w}$-RDMFT) by deriving the first functional approximations and illustrate how excitation energies can be calculated in practice. For this endeavour, we first study the symmetric Hubbard dimer, constituting the building block of the Hubbard model, for which we execute the Levy-Lieb constrained search. Second, due to the particular suitability of $\boldsymbol{w}$-RDMFT for describing Bose-Einstein condensates, we demonstrate three conceptually different approaches for deriving the universal functional in a homogeneous Bose gas for arbitrary pair interaction in the Bogoliubov regime. Remarkably, in both systems the gradient of the functional is found to diverge repulsively at the boundary of the functional's domain, extending the recently discovered Bose-Einstein condensation force to excited states. Our findings highlight the physical relevance of the generalized exclusion principle for fermionic and bosonic mixed states and the curse of universality in functional theories.
