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arXiv · 0906.1854

"Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids

F. D. M. Haldane
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Abstract

The (guiding-center) "Hall viscosity" is a fundamental tensor property of incompressible ``Hall fluids'' exhibiting the fractional quantum Hall effect; it determines the stress induced by a non-uniform electric field, and the intrinsic dipole moment on (unreconstructed) edges. It is characterized by a rational number and an intrinsic metric tensor that defines distances on an ``incompressibility lengthscale''. These properties do not require rotational invariance in the 2D plane. The sign of the guiding-center Hall viscosity distinguishes particle fluids from hole fluids, and its magnitude provides a lower bound to the coefficient of the $O(q^4)$ small-q limit of the guiding center structure factor, a fundamental measure of incompressibility. This bound becomes an equality for conformally-invariant model wavefunctions such as Laughlin or Moore-Read states.

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F. D. M. Haldane. 2009-06-10. "Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids. https://arxiv.org/abs/0906.1854

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