Entanglement Through Topological Defects: Reconciling Theory with Numerics

Abstract

Present theoretical predictions for the entanglement entropy through topological defects are violated by numerical simulations. In order to resolve this, we introduce a paradigm shift in the preparation of reduced density matrices in the presence of topological defects, and emphasize the role of defect networks with which they can be dressed. We consider the cases of grouplike and duality defects in detail for the Ising model, and find agreement with all numerically found entanglement entropies. Since our construction functions at the level of reduced density matrices, it accounts for topological defects beyond the entanglement entropy to other entanglement measures.

Figures (1)

• Figure 1: (a) Preparation of the twisted state $\vert{\phi}\rangle(t)$ in presence of the topological line $L$ (radial quantization). (b) The state is mapped to ${\cal H}_{ {\alpha\beta} }^A\otimes {\cal H}_{\beta\alpha'}^B$ by excising disks and imposing boundary conditions. Case ($ii$) is picked as an example. The length $2\pi R$ of the region $A$ is measured by a dimensionless parameter $R\in(0,1)$, so that $R=0,1$ correspond to vanishing $A$ or $B$, respectively. (c) RDM $\rho^{\phi}_{ {\alpha\beta} }$ obtained from (b) after tracing over $B$.