We unveil the existence of a two-particle bound state in the continuum (BIC) in a one-dimensional interacting nonreciprocal lattice with a generalized boundary condition. By applying the Bethe-ansatz method, we can exactly solve the wave function and eigenvalue of the bound state in the continuum band, which enable us to precisely determine the phase diagrams of BIC. Our results demonstrate that the nonreciprocal hopping can delocalize the bound state and thus shrink the region of BIC. By analyzing the wave function, we identify the existence of two types of BICs with different spatial distributions and analytically derive the corresponding threshold values for the breakdown of BICs. The BIC with similar properties is also found to exist in another system with an impurity potential.

中文翻译：

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非厄米特系统中连续体中双粒子束缚态的命运


我们揭示了在具有广义边界条件的一维相互作用非互易晶格中连续体 （BIC） 中存在双粒子束缚态。通过应用 Bethe-ansatz 方法，我们可以精确求解连续频带中束缚态的波函数和特征值，这使我们能够精确确定 BIC 的相图。我们的结果表明，非互易跳跃可以使结合态离域，从而缩小 BIC 的区域。通过分析波函数，我们确定了两种具有不同空间分布的 BICs 的存在，并分析推导出 BICs 细分的相应阈值。也发现具有相似性质的 BIC 存在于另一个具有杂质电位的系统中。