Hall Viscosity and Incompressibility of FQHE states

F. D. M. Haldane, Princeton University

The (dissipationless) "Hall viscosity" of incompressible quantum Hall fluids describes the local stress induced in the fluid by a non-uniform drift-velocity field as the linear response to a non-uniform electric field. I will describe the extension of ealier work of Avron et al. and Read (which assumes rotational invariance) to the general case (e.g. Hall fluids with a "tilted" magnetic field). Rotational invariance is NOT a generic property of QHE states, and the general formulation is very useful in exposing fundamental aspects of "Hall viscosity", including: (1) its relation to an electric dipole moment on edges that cancels a stress anomaly; (2) a relation to the SO(2,1) algebra of area-preserving guiding center deformations; (3) a clean separation into integer QHE (one-electron) and particle-hole-antisymmetric FQHE terms; (4) an unexpected relation of the FQHE part to the O(Q⁴) behavior of the guiding-center structure factor of incompressible states. The Hall viscosity also defines the fundamental metric associated with incompressibility, which characterizes the short-distance "quantum geometry" regularization of the topological field theory description.