AI 中文总结
本文研究奇异金属中费米子的纠缠熵，通过Yukawa SYK类可解模型计算子区域费米子二阶雷尼熵，揭示费米-玻色自由度纠缠的关键作用，发现其交叉行为的普适标度规律。
AI 中文摘要
对于由共形场论（CFT）描述的一维（1D）无隙系统，以及任意维度中具有费米面的自由费米子，基态纠缠熵的子系统尺寸依赖关系及其随温度向热熵的交叉行为已得到充分理解。然而，对于无准粒子的无隙费米子系统（如奇异金属），其纠缠熵的研究仍知之甚少。本文研究了一种可解的大N一维格点模型中费米子的纠缠熵，该模型类似汤川-萨赫德夫-基塔耶夫（Yukawa SYK）模型。在该模型中，两个费米点通过空间随机的汤川相互作用与标量玻色子耦合，当玻色子在量子临界点变为临界时，该模型提供了一种可解的奇异金属模型。我们精确计算了该模型中空间子区域内费米子的二阶雷尼熵。我们的结果揭示了子区域内费米子与玻色子自由度之间的纠缠，以及子区域间的纠缠，在理解这类强耦合费米-玻色系统基态方面的关键作用。我们表明，从热熵到纠缠熵的交叉行为可由单一标度假设描述，该假设将不同子区域尺寸和温度下费米子的二阶雷尼熵压缩为单一普适曲线。我们进一步表明，临界奇异金属的普适标度曲线可由标准CFT公式很好地描述，尽管其有效中心电荷远大于非相互作用情形下的值。
英文摘要
The subsystem-size dependence of ground-state entanglement entropy and its crossover to thermal entropy as a function of temperature are well understood for one-dimensional (1D) gapless systems described by conformal field theory (CFT), and for free fermions with a Fermi surface in any dimension. However, little is known about the entanglement entropy for gapless fermionic systems without quasi-particles, such as a strange metal. Here we study the entanglement entropy of fermions in a solvable large-$N$ 1D lattice model akin to the Yukawa-Sachdev-Ye-Kitaev (Yukawa SYK) model. In this model, two Fermi points are coupled to scalar bosons via spatially random Yukawa interactions, providing a solvable model of a strange metal when the bosons become critical at a quantum critical point. We exactly compute the second Rényi entropy of fermions in a spatial subregion in this model. Our results unravel crucial role of intra-subregion entanglement between fermionic and bosonic degrees of freedom along with the inter-subregion entanglement in understanding the ground states of such strongly coupled fermion-boson systems. We show that the crossover from thermal entropy to entanglement entropy, is captured by a single scaling ansatz, that collapses the second Rényi entropy of fermions for different subregion sizes and temperatures into a single universal curve. We further show that the universal scaling curve for the critical strange metal is well described by the standard CFT formula, albeit with an effective central charge substantially larger than the non-interacting value.
Comments37 pages, 18 figures
