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arXiv · 1009.4199

Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

M. Hermanns·A. Chandran·N. Regnault·B. Andrei Bernevig
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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.

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M. Hermanns, A. Chandran, N. Regnault, B. Andrei Bernevig. 2010-09-21. Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States. https://doi.org/10.1103/physrevb.84.121309

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