Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry

TL;DR

This paper explores how entanglement between anyons in topologically ordered phases can give rise to an emergent spacetime geometry resembling AdS space, providing a holographic perspective on fractionalized quantum states.

Contribution

It introduces a framework linking anyonic entanglement to emergent AdS-like geometry, extending holographic ideas to non-conformal, fractionalized systems.

Findings

Long-range entanglement between fractional charges in nanoribbons.

Embedding of entanglement structures into an AdS-like bulk geometry.

Holographic interpretation of edge correlations in topological phases.

Abstract

Intrinsically topologically ordered phases can host anyons. Here, we take the view that entanglement between anyons can give rise to an emergent geometry resembling Anti-de Sitter (AdS) space. We analyze the entanglement structure of fractionalized anyons using mutual information and interpret the results within this emergent geometric framework. As a concrete example, we consider pairs of $e/2$-charged semions that arise from instanton configurations in a disordered zigzag graphene nanoribbon. These fractional charges, located on opposite zigzag edges, show long-range quantum entanglement despite being spatially separated. We analyze the scale dependence of their entanglement and embed the ribbon into an AdS-like bulk geometry. In this setup, the entanglement structure defines minimal surfaces in the bulk, providing a geometric view of the edge correlations. This gives a holographic picture of fractionalized degrees of freedom in quasi-one-dimensional systems and shows how quantum entanglement can generate emergent geometry even without conformal symmetry.