Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization

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.

High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2609.10967 [hep-th]

(or arXiv:2609.10967v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2609.10967 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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