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arXiv · 2606.30231

Exact calculation of entanglement negativity for a 1+1D massless scalar field using phase space methods

Jason Pye·Atharva Hingane·Robert H. Jonsson
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Abstract

Quantum fields exhibit a rich entanglement structure which is still not fully understood. In this work, we study the entanglement structure of the vacuum state of a massless scalar field in (1+1)-dimensions -- a paradigmatic case for both high energy and condensed matter physics. We fully characterize the entanglement negativity between two arbitrary compact spacelike-separated regions of the field by calculating the logarithmic negativity along with the modes carrying it, called negativity cores. We achieve this using a framework based on the K\"ahler structure of Gaussian states, wherein we calculate the diagonalization of the operator associated with the partially-transposed restricted linear complex structure. In doing so, we extend the methods of this framework by proposing a basis-independent definition of the transpose operation. The explicit diagonalization we perform is enabled by a reformulation of the eigenvalue problem as a boundary value problem in the complex plane. Our results also suggest extensions to higher dimensions and fermionic fields.

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Jason Pye, Atharva Hingane, Robert H. Jonsson. 2026-06-29. Exact calculation of entanglement negativity for a 1+1D massless scalar field using phase space methods. https://arxiv.org/abs/2606.30231

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