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Geometry and the entanglement spectrum in the fractional quantum Hall effect.



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Recording Details

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PIRSA Number: 
13050049

Abstract

Fractional quantum hall states with nu = p/q  have a characteristic geometry  defined by the electric quadrupole moment of the neutral composite boson that is formed by "flux attachment" of q "flux quanta" (guiding-center orbitals) to p charged particles.    This characterizes the  "Hall viscosity".    For FQHE states described by a conformal field theory with a Euclidean metric  g_ab, the quadrupole moment is proportional to the "guiding-center spin" of the composite boson and the inverse metric.       The geometry gives rise to dipole moments at external edges or internal "orbital entanglement cuts",  and can be seen in the entanglement spectrum.