Entanglement entropy and the colored Jones polynomial

DOI10.1007/JHEP05(2018)038zbMATH Open1391.81177arXiv1801.01131OpenAlexW2781709744WikidataQ129844648 ScholiaQ129844648MaRDI QIDQ1651083

Author name not available (Why is that?)

Publication date: 11 July 2018

Published in: (Search for Journal in Brave)

Abstract: We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group $SU(2)$, the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of $U(1)$ Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for $SU(2)$ Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient $S^3$ separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure -- i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement -- i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified $SL(2,C)$ Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.

Full work available at URL: https://arxiv.org/abs/1801.01131

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Entanglement entropy and the colored Jones polynomial

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1651083)