标题： 总和与对称性分辨的纠缠谱在一些费米子CFT中来自BCFT方法 显示英文标题

标题： Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach

摘要： 在本工作中，我们使用边界共形场论（BCFT）方法研究了一些$2$维费米子共形场论中单个区间的通用总和对称性解析的纠缠谱。在此方法中，通过在纠缠边界点周围切除圆盘并施加保持所研究扩展对称性的边界条件来实现希尔伯特空间的划分。然后，约化密度矩与 BCFT 分区函数相关，并且在对称性电荷部分中也是对角的。特别是，我们首先研究了无质量狄拉克费米子和模不变$Z_2$-规范狄拉克费米子的纠缠谱，通过考虑保持轴向或矢量$U(1)$对称性的边界条件。模不变狄拉克费米子的总纠缠谱在玻色-费米对偶半径下与紧致玻色子结果相匹配，而对于无质量狄拉克费米子，发现边界熵项与自对偶紧致玻色子不匹配。发现所有情况下的对称性解析纠缠都是相同的，除了电荷谱依赖于对称性和理论。我们还通过考虑保持不同手征$U(1)^N$对称性的边界条件来研究$N$个无质量狄拉克费米子的纠缠谱。对$U(1)^M$子群的纠缠谱进行了研究，其中$M\leq N$，通过施加保持不同手征对称性的边界条件。 总纠缠谱被发现对边界理论中$U(1)^M$对称性的表示以及其他行为敏感在$O(1)$。 类似的结果也出现在对称性分辨的纠缠熵中。 对称性$U(1)$的特征$\log\log\left(\ell/\epsilon\right)$项在对称性分辨的纠缠谱中被发现与$M$成正比。 显示英文摘要

摘要： In this work, we study the universal total and symmetry-resolved entanglement spectra for a single interval of some $2$d Fermionic CFTs using the Boundary Conformal Field theory (BCFT) approach. In this approach, the partition of Hilbert space is achieved by cutting out discs around the entangling boundary points and imposing boundary conditions preserving the extended symmetry under scrutiny. The reduced density moments are then related to the BCFT partition functions and are also found to be diagonal in the symmetry charge sectors. In particular, we first study the entanglement spectra of massless Dirac fermion and modular invariant $Z_2$-gauged Dirac fermion by considering the boundary conditions preserving either the axial or the vector $U(1)$ symmetry. The total entanglement spectra of the modular invariant Dirac fermion are shown to match with the compact boson result at the Bose-Fermi duality radius, while for the massless Dirac fermion, it is found that the boundary entropy term doesn't match with the self-dual compact boson. The symmetry-resolved entanglement is found to be the same in all cases, except for the charge spectrum which is dependent on both the symmetry and the theory. We also study the entanglement spectra of $N$ massless Dirac fermions by considering boundary conditions preserving different chiral $U(1)^N$ symmetries. Entanglement spectra are studied for $U(1)^M$ subgroups, where $M\leq N$, by imposing boundary conditions preserving different chiral symmetries. The total entanglement spectra are found to be sensitive to the representations of the $U(1)^M$ symmetry in the boundary theory among other behaviours at $O(1)$. Similar results are also found for the Symmetry resolved entanglement entropies. The characteristic $\log\log\left(\ell/\epsilon\right)$ term of the $U(1)$ symmetry is found to be proportional to $M$ in the symmetry-resolved entanglement spectra.