Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

TL;DR

This paper proposes that the level counting in the orbital entanglement spectra of finite Laughlin FQH states follows Haldane statistics, revealing a topological number and universal properties of the quantum Hall states.

Contribution

It introduces a conjecture linking entanglement spectra counting to Haldane statistics, providing a new topological invariant for FQH states.

Findings

Numerical evidence supports the Haldane statistics conjecture.

The entanglement gap protects a universal statistical property.

The boson compactification radius is identified as a topological number.

Abstract

We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets at filling $\nu=1/m$ is described by the Haldane statistics of particles in a box of finite size. This principle explains the observed deviations of the OES counting from the edge-mode conformal field theory counting and directly provides us with a topological number of the FQH states inaccessible in the thermodynamic limit- the boson compactification radius. It also suggests that the entanglement gap in the Coulomb spectrum in the conformal limit protects a universal quantity- the statistics of the state. We support our conjecture with ample numerical checks.