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

Understand

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.