论文标题
Sachdev-ye-Kitaev模型中的量子纠缠及其概括
Quantum Entanglement in the Sachdev-Ye-Kitaev Model and its Generalizations
论文作者
论文摘要
纠缠是量子物理学中最重要的概念之一。我们回顾了使用大型$ N $可解决模型在多体系统中理解量子纠缠方面的最新进展：Sachdev-Ye-Kitaev（Syk）模型及其概括。我们使用三种不同的方法介绍了原始SYK模型中纠缠熵的研究：确切的对角线化，本征态热假设和路径积分表示。对于耦合的SYK模型，纠缠熵在热值下显示线性生长和饱和。饱和度与重力中的复制虫孔有关。最后，我们考虑在重复测量下量子多体系统的稳态纠缠熵。扩大复制空间中传统的对称性破裂导致测量引起的纠缠相变。
Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-$N$ solvable models: the Sachdev-Ye-Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK Model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.
