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Entanglement in $(1+1)$-dimensional Free Scalar Field Theory: Tiptoeing between Continuum and Discrete Formulations

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arxiv 2406.11031 v2 pith:TV7TXRL7 submitted 2024-06-16 hep-th math-phmath.MPquant-ph

Dimitrios Katsinis , Georgios Pastras This is my paper · ORCID
classification hep-thmath-phmath.MPquant-ph
keywords theoryentanglemententropyfieldfreehamiltonianmodularcontinuous
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abstract

We review some classic works on ground state entanglement entropy in $(1+1)$-dimensional free scalar field theory. We point out identifications between the methods for the calculation of entanglement entropy and we show how the formalism developed for the discretized theory can be utilized in order to obtain results in the continuous theory. We specify the entanglement spectrum and we calculate the entanglement entropy for the theory defined on an interval of finite length $L$. Finally, we derive the modular Hamiltonian directly, without using the modular flow, via the continuous limit of the expressions obtained in the discretized theory. In a specific coordinate system, the modular Hamiltonian assumes the form of a free field Hamiltonian on the Rindler wedge.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement Entropy of a Scalar Field in Anti-de Sitter Space

    hep-th 2025-05 conditional novelty 7.0 of 10

    For a free massive scalar in AdS4, the UV-divergent entanglement entropy of centered spherical regions takes a fitted form whose logarithmic coefficient, -1/90 plus (-mu^2 a^2/6 - 1/3) times the proper area, matches c...

  2. Boundary Conditions and Entanglement in Anti-de Sitter Space

    hep-th 2026-08 conditional novelty 6.0 of 10

    For a conformally coupled scalar in AdS4, the UV-divergent entanglement entropy is independent of boundary conditions, while the UV-finite part acquires a boundary-condition dependent R^2/a^2 correction with coefficie...

  3. Entanglement on a Sphere

    hep-th 2025-07 conditional novelty 6.0 of 10

    The entanglement entropy of a scalar field on the R×S^3 Einstein universe has an infrared contribution from the zero mode with coefficient c_IR = 1/6, distinct from the de Sitter value 1/3.

  4. A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory

    hep-th 2025-02 conditional novelty 4.0 of 10

    For a free massive scalar field in 1+1 dimensions, the Araki-Uhlmann relative entropy between a coherent state and the vacuum decreases with mass and increases with region size in numerical tests.

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