Symmetry Resolved Entanglement Entropy in Hyperbolic de Sitter Space

TL;DR

This paper investigates how internal symmetries affect entanglement entropy in de Sitter space, revealing that symmetry-resolved entanglement exhibits equipartition in the large volume limit for free scalar and Dirac fields.

Contribution

It introduces the analysis of symmetry-resolved entanglement entropy in de Sitter space for free fields, showing equipartition and its breaking at finite volumes.

Findings

Symmetry-resolved entanglement entropy exhibits equipartition in large volume limit.

Equipartition is broken by terms of order 1/V_{H_3} at finite volumes.

Results apply to free complex scalar and Dirac fields with U(1) symmetry.

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 $U(1)$ 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 $V_{H_3}^0$ in the limit of large $V_{H_3}$, where $V_{H_3}$ is the volume of either region. This equipartition however is only broken by the terms of order $O(1/V_{H_3})$. Consequently, we have equipartition of symmetry resolved entanglement entropy in the limit of infinite volume.