Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization

• URL: http://arxiv.org/abs/2609.10967v1
• Date: Thu, 10 Sep 2026 01:37:49 GMT
• Title: Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization
• Abstract summary: We investigate timelike entanglement in quantum field theory using spacetime density matrix.<n>We find quantitative agreement in both magnitude and phase across distinct causal regimes.<n>These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.
• Score: 4.363749106659002
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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