双缩放SYK中的半经典纠缠楔

中文摘要 AI 辅助

我们研究了双缩放SYK中部分纠缠热态的纠缠结构，允许由物质插入所携带的风味自由度处于任意混合态。在半经典极限下，随后是重探针极限，我们的replica计算给出了Faulkner--Lewkowycz--Maldacena公式：边界熵分解为一个‘面积’项（与风味态无关）和相应纠缠楔中的体物质熵。改变算子插入的欧几里得位置会在边界熵中产生尖锐的转变，我们将其解释为单个物质激发穿过楔的边界，因此是明确定义的纠缠楔的证据。为了推导这一结果，我们分析了一般欧几里得$2n$点函数的半经典行为，并给出了它们分解为两点函数乘积之和的概率性证明。我们还从精确谱表示中给出了一个互补的推导，使用了量子$6j$符号的半经典行为。

英文摘要

We study the entanglement structure of partially entangled thermal states in double-scaled SYK , allowing flavor degrees of freedom carried by matter insertions to be in an arbitrary mixed state. In the semiclassical limit, followed by the heavy-probe limit, our replica calculation gives a Faulkner--Lewkowycz--Maldacena formula: the boundary entropy decomposes into an `area' term (independent of the flavor state) and the bulk matter entropy in a corresponding entanglement wedge. Varying the Euclidean locations of the operator insertions produces sharp transitions in the boundary entropy, which we interpret as individual matter excitations crossing the boundary of the wedge and hence as evidence for a sharply defined entanglement wedge. To derive this result, we analyze the semiclassical behavior of general Euclidean $2n$-point functions and give a probabilistic proof of their factorization into sums over products of two-point functions. We also give a complementary derivation from exact spectral representations, using the semiclassical behavior of the quantum $6j$-symbol.

发表机构

• University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
• Massachusetts Institute of Technology（麻省理工学院）

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