电子在分子网络中的跳跃：光谱与对称性
Electrons Hopping across a Molecular Network: Spectra and Symmetries
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中文总结 AI 辅助
研究有限分子环网络上无自旋电子，分析晶格几何等相互作用，用群论方法结合外部磁通量研究光谱演化，确定粒子数奇偶系统区别，发现半填充时粒子 - 空穴对称性可保护对称扇区免受塞曼分裂。
中文摘要 AI 辅助
我们研究了由紧束缚哈伯德哈密顿量描述的有限分子环网络上相互作用的无自旋电子。分析了具有\(L = 3,4,5,6\)个节点、填充一、二或三个电子的环中晶格几何、库仑相互作用和离散对称性之间的相互作用。特别关注网络对称性在确定多体光谱结构和本征态的穆利肯分类中的作用。使用群论方法，研究了外部磁通量存在下光谱的演化。塞曼效应消除简并，并与库仑相互作用导致对称扇区中的避免交叉。我们确定了粒子数为偶数和奇数的系统之间的定性区别。在半填充时，粒子 - 空穴对称性（对偶性）保护选定的对称扇区免受塞曼分裂。
英文摘要
We investigate interacting spinless electrons on finite molecular ring networks described by a tight-binding Hubbard Hamiltonian. The interplay between lattice geometry, Coulomb interactions and discrete symmetries is analysed for rings with $L=3,4,5,6$ nodes, filled with one, two or three electrons. Special attention is devoted to the role of the network symmetries in determining the structure of the many-body spectrum and the Mulliken classification of the eigenstates. Using group-theoretical methods, we examine the evolution of the spectra in the presence of an external magnetic flux. The Zeeman effect lifts degeneracies and results in combination with the Coulomb interaction to avoided crossings in symmetry sectors. We identify a qualitatively distinction between systems with an even and odd number of particles. At half-filling, particle-hole symmetry (duality) protects selected symmetry sectors against Zeeman splitting.
