Entanglement entropy in fermionic Laughlin states

TL;DR

This paper analyzes bipartite entanglement entropy in fermionic Laughlin states, linking orbital partitioning to topological properties and interpreting particle partitioning through exclusion statistics.

Contribution

It provides analytic and numerical insights into entanglement entropy in fractional quantum Hall states, connecting orbital and particle partitions to topological and statistical features.

Findings

Orbital partitioning relates to the topological quantum dimension.

A close upper bound for particle entanglement entropy is established.

Interpretation of entanglement in terms of exclusion statistics.

Abstract

We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the `total quantum dimension') characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.