论文标题
Chern-Simons理论中具有有限规组的多边界纠缠
Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
论文作者
论文摘要
我们研究了（1+1）和（2+1）尺寸的Chern-Simons理论，具有有限的离散量规组$ g $。 （1+1） - $ d $中的各州与属$ g $的Riemann表面与多个$ S^1 $边界有关，我们使用副本技巧来计算此类州的纠缠熵。在（2+1）-$ d $中，我们专注于与圆环链接补充相关的状态，这些状态与Hilbert Space的张量产品相关联，与多个$ t^2 $相关。我们对阿贝利亚人和非阿贝尔群体的纠缠结构进行了定量分析。对于这项工作中考虑的所有状态，我们发现组直接乘积的纠缠熵是单个组的熵的总和，即$ \ text {ee}（g_1 \ times g_2）= \ text {ee}（g_1）+\ text {ee}（g_1）+\ text {ee}（ee}（g_2）$。此外，通过追踪希尔伯特空间的一部分获得的降低密度矩阵在其余希尔伯特空间的任何两部分中都具有正分半偏移式的正向。
We study the multi-boundary entanglement structure of the states prepared in (1+1) and (2+1) dimensional Chern-Simons theory with finite discrete gauge group $G$. The states in (1+1)-$d$ are associated with Riemann surfaces of genus $g$ with multiple $S^1$ boundaries and we use replica trick to compute the entanglement entropy for such states. In (2+1)-$d$, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple $T^2$. We present a quantitative analysis of the entanglement structure for both abelian and non-abelian groups. For all the states considered in this work, we find that the entanglement entropy for direct product of groups is the sum of entropy for individual groups, i.e. $\text{EE}(G_1 \times G_2) = \text{EE}(G_1)+\text{EE}(G_2)$. Moreover, the reduced density matrix obtained by tracing out a subset of the total Hilbert space has a positive semidefinite partial transpose on any bi-partition of the remaining Hilbert space.
