Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1998-04-17
Nucl.Phys.B532:783-806,1998
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Latex,21 pages.version to appear in Nucl.Phys.B
Scientific paper
10.1016/S0550-3213(98)00598-7
We investigate the modular properties of the characters which appear in the partition functions of nonabelian fractional quantum Hall states. We first give the annulus partition function for nonabelian FQH states formed by spinon and holon (spinon-holon state). The degrees of freedom of spin are described by the affine SU(2) Kac-Moody algebra at level $k$. The partition function and the Hilbert space of the edge excitations decomposed differently according to whether $k$ is even or odd. We then investigate the full modular properties of the extended characters for nonabelian fractional quantum Hall states. We explicitly verify the modular invariance of the annulus grand partition functions for spinon-holon states, the Pfaffian state and the 331 states. This enables one to extend the relation between the modular behavior and the topological order to nonabelian cases. For the Haldane-Rezayi state, we find that the extended characters do not form a representation of the modular group, thus the modular invariance is broken.
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