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arXiv 2402.07557hep-thquant-ph
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基于BCFT方法的某些费米子CFT中的全纠缠谱与对称性分辨纠缠谱

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

Himanshu Gaur

备注：
v2, 27 pages, 2 figures, improved presentation, typos corrected, references added. Accepted for publication in JHEP
发表信息：
JHEP09(2024)173
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AI总结：

本文使用BCFT方法研究了某些2维费米子CFT中单个区间的全纠缠谱与对称性分辨纠缠谱，发现模不变Dirac费米子的全纠缠谱与对偶半径处紧致玻色子结果匹配，且U(1)对称性的特征loglog(ℓ/ε)项在对称性分辨纠缠谱中与M成正比。

摘要：

在本研究中，我们使用边界共形场论（BCFT）方法，研究了某些2维费米子共形场论（CFT）中单个区间的普适全纠缠谱与对称性分辨纠缠谱。在该方法中，希尔伯特空间的划分是通过在纠缠边界点周围切出圆盘并施加保持所研究的扩展对称性的边界条件来实现的。约化密度矩随后与BCFT配分函数相关联，并且发现在对称性荷扇区中是对角化的。特别地，我们首先通过考虑保持轴矢或矢量U(1)对称性的边界条件，研究了无质量Dirac费米子和模不变的Z_2规范Dirac费米子的纠缠谱。模不变Dirac费米子的全纠缠谱被证明与Bose-Fermi对偶半径处的紧致玻色子结果相匹配，而对于无质量Dirac费米子，发现边界熵项与自对偶紧致玻色子不匹配。发现在所有情况下对称性分辨纠缠都是相同的，除了依赖于对称性和理论的荷谱。我们还通过考虑保持不同手征U(1)^N对称性的边界条件，研究了N个无质量Dirac费米子的纠缠谱。通过施加保持不同手征对称性的边界条件，研究了U(1)^M子群（其中M≤N）的纠缠谱。发现全纠缠谱对边界理论中U(1)^M对称性的表示以及O(1)量级的其他行为敏感。对于对称性分辨纠缠熵也发现了类似的结果。发现U(1)对称性的特征loglog(ℓ/ε)项在对称性分辨纠缠谱中与M成正比。

英文摘要：

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 $\log\log\left(\ell/ε\right)$ term of the $U(1)$ symmetry is found to be proportional to $M$ in the symmetry-resolved entanglement spectra.

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