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

• URL: http://arxiv.org/abs/2606.30231v1
• Date: Mon, 29 Jun 2026 12:44:17 GMT
• Title: Exact calculation of entanglement negativity for a 1+1D massless scalar field using phase space methods
• Abstract summary: We study the entanglement structure of the vacuum state of a massless scalar field in (1+1)-dimensions.<n>We fully characterize the entanglement negativity between two arbitrary compact spacelike-separated regions of the field.<n>Our results also suggest extensions to higher dimensions and fermionic fields.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Kähler 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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