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.
Related
- Frenet--Serret invariants of timelike worldlines in Kerr spacetime: chart independence, horizon crossing and null-endpoint limits
- Timelike Entanglement First Law and Linearized Field Equations in Higher Curvature Gravity
- Timelike entanglement first law and linearized field equations in higher curvature gravity
- Modular Flow and Holographic Timelike Entanglement Entropy in AdS and Flat Holography
- Aspects of holographic timelike entanglement entropy in black hole backgrounds
BibTeX
@misc{wang2026timelike,
title = {{Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization}},
author = {Hao-yu Wang and Wu-zhong Guo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10967},
eprint = {2609.10967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10967},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization
AU - Hao-yu Wang
AU - Wu-zhong Guo
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.10967
UR - https://arxiv.org/abs/2609.10967
AB - 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.
ER -