论文标题
边界对对称性解决纠缠的影响
Boundary effects on symmetry resolved entanglement
论文作者
论文摘要
我们研究具有边界的一维系统中的对称性解决的纠缠熵。我们为保形不变理论提供了一些一般结果，然后转移到半无限的自由费米子链中。我们考虑从边界开始并远离它的间隔。我们根据定理和猜想的toeplitz+hankel矩阵的光谱得出了带电和对称性的熵的精确公式。在表征远离边界的间隔的途径中，我们证明了Toeplitz+Hankel矩阵的特征值与阻止Toeplitz的特征值之间的一般关系。一个重要的方面是，从充电到对称性熵的鞍点近似将代数校正引入比例比没有边界的系统中要严重得多。
We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En route to characterise the interval away from the boundary, we prove a general relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz ones. An important aspect is that the saddle-point approximation from charged to symmetry resolved entropies introduces algebraic corrections to the scaling that are much more severe than in systems without boundaries.
