Bulk Entanglement and Boundary Spectra in Gapped Topological Phases
Year: 2018
Type: preprint
Abstract: We study the correspondence between boundary spectrum of non-chiral topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed manifold. The closed manifold is bipartitioned into two subsystems, one of which has the same topology as $\mathcal{M}$. Specifically, we focus on the case of generalized string-net models and discuss the cases where $\mathcal{M}$ is a disk or a cylinder. The correspondence turns out to be very different from that of the chiral topological orders. When $\mathcal{M}$ has the topology of a cylinder, different boundary conditions of the cylinder will correspond to different entanglement cuts on the torus. Charge (smooth) and flux (rough) boundaries of toric code, more general $\mathbb{Z}_N$ models, and the simplest non-abelian case of doubled Fibonacci are demonstrated.
Source: arXiv (Cornell University)
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2809106825