Yu Xue-Jia, Yang Sheng, Lin Hai-Qing, Jian Shao-Kai
Department of Physics, <a href="https://ror.org/011xvna82">Fuzhou University</a>, Fuzhou 350116, Fujian, China.
Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, <a href="https://ror.org/011xvna82">Fuzhou University</a>, Fuzhou, Fujian 350108, China.
Phys Rev Lett. 2024 Jul 12;133(2):026601. doi: 10.1103/PhysRevLett.133.026601.
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.
量子纠缠是拓扑态的一个决定性特征。然而，对于没有体能隙的拓扑态，纠缠谱仍未得到充分探索。通过结合场论和数值技术，我们精确计算并分析了一维无隙对称保护拓扑态的纠缠谱。我们强调，通用纠缠谱不仅编码了非平凡的边缘简并度，将李 - 霍尔丹猜想推广到了无隙拓扑态，还包含了底层边界共形场论的算符内容。这意味着体态波函数可以作为无隙对称保护拓扑态中量子临界性和拓扑的指纹。我们还识别出了一种超越传统共形边界条件的对称性增强共形边界条件。
