Entanglement Negativity and Topological Degeneracy*

We study the spatial distribution of entanglement in (2+1)d topological phases. Specifically, we use the coupled-wire construction to study the logarithmic negativity[1] for various spatial partitions of the ground state. We show how monogamy-type relations [2,3] for the logarithmic negativity can reveal the degeneracy of the ground state wave functions on a torus.

References:
[1] G. Vidal and R.F. Werner. A computable measure of entanglement. https://arxiv.org/pdf/quant- ph/0102117.pdf, Feburary 2001.
[2] Patrick Hayden, Richard Jozsa, Dénes Petz, and Andreas Winter. Structure of states which satisfy strong subadditivity of quantum entropy with equality. https://arxiv.org/pdf/quant- ph/0304007.pdf, August 2003
[3] Huan He and Guifre Vidal. Disentangleing theorem and monogamy for entanglement negativity.https://arxiv.org/pdf/1401.5843.pdf, January 2014.