Typical entanglement in anyon chains: Page curves beyond Lie group symmetries

TL;DR

This paper analyzes bipartite entanglement in one-dimensional anyon chains constrained by fusion rules, deriving analytical expressions and demonstrating typicality and universality in chaotic regimes.

Contribution

It generalizes symmetry-resolved entanglement entropy to quantum groups and establishes the anyonic Page curve as a benchmark for chaos in topological systems.

Findings

Analytical expressions for average and variance of anyonic entanglement entropy.

Large system size expansion shows no universal symmetry corrections except topological.

Chaotic eigenstates match Haar-random predictions, confirming entanglement as a chaos indicator.

Abstract

We study bipartite entanglement statistics in one-dimensional anyon chains, whose Hilbert spaces are constrained by fusion rules of unitary pre-modular categories. Our setup generalizes previous frameworks on symmetry-resolved entanglement entropy for non-abelian Lie group symmetries to the setting of quantum groups. We derive analytical expressions for the average anyonic entanglement entropy and its variance. Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(\sqrt{L})$ or $O(1)$ symmetry-type corrections except for a subleading topological correction term that produces a Page curve asymmetry. We further show that the variance decays exponentially with system size, establishing the typicality. Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions, supporting the use of eigenstate entanglement as a diagnostic of quantum chaos. Our results establish the anyonic Page curve as an appropriate chaotic benchmark in topological many-body systems and connect anyonic entanglement to Page-type universality in quantum many-body physics.