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Algebraic Aspects of the Fractional Quantum Hall Effect

Dimitra Karabali
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Abstract

Some algebraic issues of the FQHE are presented. First, it is shown that on the space of Laughlin wavefunctions describing the $ν=1/m$ FQHE, there is an underlying $W_{\infty}$ algebra, which plays the role of a spectrum generating algebra and expresses the symmetry of the ground state. Its generators are expressed in a second quantized language in terms of fermion and vortex operators. Second, we present the naturally emerging algebraic structure once a general two-body interaction is introduced and discuss some of its properties.

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Dimitra Karabali. 1993-09-28. Algebraic Aspects of the Fractional Quantum Hall Effect. https://doi.org/10.1016/0550-3213(94)90339-5

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