Work

Haldane statistics in the finite-size entanglement spectra of 1/ m fractional quantum Hall states

Year: 2011

Type: article

Abstract: We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-size Laughlin fractional quantum Hall (FQH) droplets at filling $\ensuremath{\nu}=1/m$ 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 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.

Source: Physical Review B

DOI: 10.1103/physrevb.84.121309

Authors: M. Hermanns, A. Chandran, N. Regnault, B. Andrei Bernevig

Institutions: Princeton University, Centre National de la Recherche Scientifique, École Normale Supérieure - PSL, Laboratoire de Physique de l'Ecole Normale Supérieure

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, Division of Materials Research

Awards: CAREER: Emergent Phenomena in New Quantum Materials, G6711204355