We study the entanglement entropy, the Rényi entropy, and the mutual (Rényi) information of Dirac fermions on a 2 dimensional torus in the presence of constant gauge fields. We derive their general formulas using the equivalence between twisted boundary conditions and the background gauge fields. Novel and interesting physical consequences have been presented in arXiv:1705.01859. Here we provide detailed computations of the entropies and mutual information in a low temperature limit, a large radius limit, and a high temperature limit. The high temperature limit reveals rather different physical properties compared to those of the low temperature one: there exist two non-trivial limits that depend on a modulus parameter and are not smoothly connected.

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Published in Journal of High Energy Physics, v. 2017, issue 8, article no. 41, p. 1-35.

© The Author(s) 2017

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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This work is partially supported by NSF Grant PHY-1214341. Article funded by SCOAP3