AI 中文总结
研究(1+1)维共形场论中空间区间固定结果投影测量后低能激发态的纠缠，通过复制狭缝几何到圆盘，将激发态对测量后Rényi熵的贡献表示为归一化边界共形场论关联函数，并应用于紧致自由玻色子共形场论。
AI 中文摘要
我们研究(1+1)维共形场论（CFT）中在空间区间上进行固定结果投影测量后低能激发态的纠缠。后选测量结果由携带共形边界条件的狭缝表示，而激发态通过在欧几里得路径积分中插入算符引入。将复制的狭缝几何映射到圆盘后，激发态对测量后Rényi熵的贡献表示为归一化边界共形场论关联函数。我们将此框架应用于紧致自由玻色子共形场论。对于手征流激发，相关比率由电流hafnians给出。我们还研究了\(J\)和\(\bar J\)以及共轭紧致顶点算符的相干叠加。在共轭顶点的情况下，普通圆柱的第二个Rényi比率与相对相位无关，而有限狭缝测量后的比率包含相位敏感的干涉项。最后，我们描述了用于在临界XX链中测试这些预测的自由费米子和多斯莱特行列式方法。
英文摘要
We study the entanglement of low-energy excited states after a fixed-outcome projective measurement on a spatial interval in a (1+1)-dimensional conformal field theory (CFT). We restrict to post-selected measurement outcomes whose induced boundary condition flows in the infrared to a conformal boundary condition. Such an outcome is represented by a slit carrying that boundary condition, while excited states are introduced by operator insertions in the Euclidean path integral. After mapping the replicated slit geometry to a disk, the excited-state contribution to the post-measurement Rényi entropy is expressed as a normalized boundary-CFT correlation function. We apply this framework to the compact free boson CFT. For the chiral current excitation, the relevant ratios are given by current hafnians. We also study coherent superpositions of $J$ and $\bar J$, and of conjugate compact vertex operators. In the conjugate-vertex case, the ordinary-cylinder second Rényi ratio is independent of the relative phase, whereas the finite-slit post-measurement ratio contains phase-sensitive interference terms. Finally, we describe free-fermion and multi-Slater determinant methods for testing these predictions in the critical XX chain.
Comments34 pages, 3 figures, revised version
