Symmetry Resolved Entanglement Entropy in Hyperbolic de Sitter Space
arXiv:2211.11218 · doi:10.1103/PhysRevD.107.125008
Abstract
In this paper, we study the relation between entanglement and global internal symmetries on de Sitter space. We consider two symmetric causally disconnected regions in the hyperbolic chart on de Sitter space. Since entanglement measures characterises correlations, the study of entanglement between the two causally disconnected regions gives information about the long range correlations in de Sitter space. When a theory possesses an additive global internal symmetry, the entanglement measures for a state with fixed global charge may be decomposed into local charge sectors in either subsystem and thus providing a finer resolution of entanglement. Here we will consider two theories: free complex scalar field, and free Dirac field on de Sitter space. Both theories possess global internal symmetry. We study the symmetry resolved entanglement entropy for both theories in the Bunch-Davies vacuum state. We find that the symmetry resolved entanglement entropy has equipartition into local charge sectors upto the terms that scale as in the limit of large , where is the volume of either region. This equipartition however is only broken by the terms of order . Consequently, we have equipartition of symmetry resolved entanglement entropy in the limit of infinite volume.
arXiv commentv2, 15 pages, 3 figures; Typos corrected; Figure 2, and Figure 3 modified; Discussions and new references added; Results unchanged; Accepted for publication in PRD
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