Topological Entanglement in Abelian and non-Abelian Excitation Eigenstates

TL;DR

This paper reveals that the entanglement spectrum of fractional quantum Hall excitations, not just ground states, encodes topological order and distinguishes between different conformal field theory sectors, including non-Abelian quasiholes.

Contribution

It demonstrates that the entanglement spectrum of quasihole excitations can identify topological order and sector changes, extending entanglement analysis beyond ground states.

Findings

Entanglement spectrum differentiates CFT sectors via quasihole positions.

QH entanglement level counting matches CFT predictions in the thermodynamic limit.

Sector changes occur as non-Abelian quasiholes cross the entanglement cut.

Abstract

Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the \emph{excitations} of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.