Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a ‘truncation scheme’. This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a 1 + 1D causal diamond in Minkowski spacetime. We present new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We extend previous results in the massless theory to include Rényi entropies and include new results for the massive theory. We also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.

中文翻译：

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对 1 + 1 维因果集中的纠缠熵的见解

因果集中的纠缠熵提供了量子场自由度的基本协变特征。在这种情况下的一个已知结果是，除了一些没有类似连续体的贡献之外，自由度还包括许多具有类似连续体类似物的贡献。后者表现出离散性尺度以下的特征，并使用“截断方案”从纠缠熵中排除。这种截断对于恢复纠缠熵的标准空间面积定律是必要的。在这篇论文中，我们建立在之前关于无质量标量场纠缠熵的工作的基础上，该因果集近似于 Minkowski 时空中的 1 + 1D 因果钻石。我们对截断的贡献提出了新的见解，包括证据表明它们表现为波动并编码特定于特定因果集散布的特征。我们扩展了先前在无质量理论中的结果，以包括 Rényi 熵，并包括有质量理论的新结果。我们还讨论了我们的工作对在更一般情况下处理因果集中的纠缠熵的意义。