Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

Details Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

2010-09-21

arxiv.org/abs/1009.4199v2

Phys. Rev. B 84, 121309(R) (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

4.1 pages, published version

Scientific paper

10.1103/PhysRevB.84.121309

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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