类时间纠缠来自时空密度矩阵：一个格点实现
Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization
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中文总结 AI 辅助
本文通过时空密度矩阵在格点上实现类时间纠缠，推广高斯对角化方法计算非厄米谱，并用相关函数验证，为类时间纠缠提供微观基础。
中文摘要 AI 辅助
我们利用时空密度矩阵研究量子场论中的类时间纠缠，并提供了一个微观格点实现。对于二维自由实标量场，我们将高斯对角化方法推广到一般非厄米的约化时空密度矩阵，并在一般正则情形下确定其完整的非零谱，以及所有整数Rényi矩。实时复制构造将这些矩与洛伦兹分支点扭曲算符关联函数等同起来。我们针对圆上的完整四点函数、具有狄利克雷和诺伊曼边界条件的边界两点函数以及大质量形状因子预测检验了这一等同关系，在不同因果区域中发现了幅度和相位上的定量一致。边界设置展示了一个有限的因果连通窗口，在该窗口中每个整数Rényi熵都是实数，表明实在性并不等同于因果断开。这些结果为类时间纠缠以及超出等时区域的洛伦兹扭曲算符方法提供了微观格点基础。
英文摘要
We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer Rényi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer Rényi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.
发表机构
- School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
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