Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett.2003, 90, 013001]. It was also found that these states are destroyed within the Born–Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original 2D two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove the GP within a two-state problem. Using the stabilization graph technique we have shown that the GP is crucial for emergence of BSCs.

中文翻译：

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具有圆锥形相交的系统的连续体中束缚态的拓扑起源

在具有圆锥形交点（CI）的线性振动耦合模型中，报告了连续体（BSC）的束缚态[Cederbaum等。物理 莱特牧师 2003，90，013001]。还发现这些状态在Born–Oppenheimer近似（BOA）中被破坏。我们调查与CI相关的非平凡的拓扑阶段或几何阶段（GP）是否负责BSC。为了解决这个问题，我们探索了对支持BSC的原始2D二维线性线性振动耦合模型的修改。这些修改可以在BOA之后添加GP效果，也可以在两个状态的问题中删除GP。使用稳定图技术，我们已经证明了GP对于BSC的出现至关重要。