标题： 无能隙对称保护拓扑态中的普适纠缠谱 显示英文标题

标题： Universal entanglement spectrum in gapless symmetry protected topological states

摘要： 量子纠缠标志着拓扑态的一个确定性特征。 然而，对于没有体能隙的拓扑态，纠缠谱仍然研究不足。 通过场论和数值技术的结合，我们准确计算并分析了一维无能隙对称保护拓扑态的纠缠谱。 我们强调，普遍的纠缠谱不仅编码了非平凡的边缘简并性，将Li-Haldane猜想推广到无能隙拓扑态，还包含了底层边界共形场理论的算符内容。 这意味着，体波函数可以作为无能隙对称保护拓扑态中量子临界性和拓扑性的指纹。 我们还识别出一种超越传统共形边界条件的对称丰富共形边界条件。 显示英文摘要

摘要： Quantum entanglement marks a definitive feature of topological states. However, the entanglement spectrum remains insufficiently explored for topological states without a bulk energy gap. Using a combination of field theory and numerical techniques, we accurately calculate and analyze the entanglement spectrum of gapless symmetry protected topological states in one dimension. We highlight that the universal entanglement spectrum not only encodes the nontrivial edge degeneracy, generalizing the Li-Haldane conjecture to gapless topological states, but also contains the operator content of the underlying boundary conformal field theory. This implies that the bulk wave function can act as a fingerprint of both quantum criticality and topology in gapless symmetry protected topological states. We also identify a symmetry enriched conformal boundary condition that goes beyond the conventional conformal boundary condition.