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Boson-fermion mapping and off-diagonal long-range order in fractional quantum Hall effect

1991; American Physical Society; Volume: 66; Issue: 3 Linguagem: Inglês

10.1103/physrevlett.66.389

1092-0145

Xin Xie, Song He, S. Das Sarma,

Physics of Superconductivity and Magnetism

A new nonsingular mapping between bosons and fermions is introduced in connection with the fractional quantum Hall effect. The mapping connects a fermion system of filling ${\ensuremath{\nu}}_{\mathit{f}}$ to a boson system of filling ${\ensuremath{\nu}}_{\mathit{b}}$ through the relation ${\ensuremath{\nu}}_{\mathit{f}}^{\mathrm{\ensuremath{-}}1}$=${\ensuremath{\nu}}_{\mathit{b}}^{\mathrm{\ensuremath{-}}1}$+1. The ground state of the boson system is shown to map accurately to that of the fermion system if and only if they are both incompressible quantum Hall states. The accuracy of the mapping is shown to be related to the validity of the mean-field theory. The relevance of this mapping to off-diagonal long-range order is discussed by numerically studying the binding of wave-function zeros to particle positions.