Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State

TL;DR

This paper uses matrix product states to analyze symmetry-resolved entanglement in a non-Abelian quantum Hall state, revealing entanglement distribution patterns and confirming theoretical predictions.

Contribution

It provides the first detailed numerical study of symmetry-resolved entanglement in a non-Abelian quantum Hall state, including a comparison with Li-Haldane conjecture predictions.

Findings

Approximate entanglement equipartition among symmetry sectors.

Validation of symmetry-resolved entanglement expectations in non-Abelian states.

Agreement between entanglement spectrum and Li-Haldane conjecture predictions.

Abstract

Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting statistics and symmetry-resolved entanglement entropies. Our results reveal an approximate equipartition of entanglement among symmetry sectors, consistent with theoretical expectations and subject to finite-size corrections. The results also show that these expectations for symmetry-resolved entanglement entropy remain valid in the case of a non-Abelian state where the topological sectors cannot be distinguished by the Abelian $\mathrm{U}(1)$ symmetry alone, and where neutral and charged modes possess distinct velocities. We additionally perform a detailed comparison of the entanglement spectrum with predictions from the Li-Haldane conjecture, finding remarkable agreement, and enabling a more precise understanding of the effects of the distinct neutral and charged velocities. This not only provides a stringent test of the conjecture but also highlights its explanatory power in understanding the origin and structure of finite-size effects across different symmetry sectors.