存在拓扑界面和对偶性时的纠缠
Entanglement in Presence of Topological Interfaces and Dualities
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中文总结 AI 辅助
研究二维共形场论中通过拓扑缺陷的纠缠，基于新框架，通过研究自由玻色子CFT缺陷提供新例，扩展框架到连接不同CFT的拓扑界面，表明对偶性界面约化密度矩阵是真空投影，用相对熵量化可区分性。
中文摘要 AI 辅助
通过界面的纠缠在二维共形场论（CFT）中备受关注。然而，基于现有框架的场论预测通常与数值结果不兼容。近期提出了一个通过拓扑缺陷的纠缠新框架，能成功重现伊辛模型在所有测试情形和区域的数值结果。本文有两个目标，一是通过研究自由玻色子CFT中的缺陷提供新例子，二是将框架扩展到连接两个可能不同CFT的拓扑界面，特别是对偶理论相关的界面。我们表明对偶性界面的约化密度矩阵是真空约化密度矩阵在单个对称扇区上的投影，相对熵可量化其与真空约化密度矩阵的可区分性。
英文摘要
Entanglement through interfaces has attracted considerable attention in 2d conformal field theory (CFT). However, it is known that field-theoretic predictions based on the existing framework are in general incompatible with numerical results [1-4]. A new framework for entanglement through topological defects was recently proposed in [5]. It provides a general description of entanglement through topological defects and successfully reproduces the numerical results for the Ising model in all tested cases and regimes. The key insight is that the relevant quantum correlations are encoded in twisted states, allowing for the construction of the full reduced density matrix (RDM). In this work we pursue two objectives. First, we provide new examples by studying defects in the free boson CFT. Second, we extend the framework to topological interfaces connecting two, possibly distinct, CFTs. Of particular interest are interfaces relating dual theories. We show that the reduced density matrix for a duality interface is the projection of the vacuum reduced density matrix onto a single symmetry sector, closely paralleling the framework of symmetry resolution. Unlike symmetry resolution, however, the projection is imposed by the physical interface itself, demonstrating that duality interfaces reflect quantum correlations back into the entangling interval. We establish this mechanism for diagonal and non-diagonal rational CFTs as well as the free boson CFT. Relative entropy allows us to quantify the distinguishability of the duality interface RDM from the vacuum RDM.
