Hall viscosity as a topological invariant

TL;DR

This paper explores the topological nature of Hall viscosity in quantum Hall states, linking it to a generalized invariant derived from Green's functions that extends to interacting systems.

Contribution

It introduces a topological invariant based on Green's functions that generalizes Hall conductance to interacting fractional Hall states and relates it to Hall viscosity.

Findings

Invariant equals twice the total orbital spin in fractional Hall states

Links Hall viscosity to a topological invariant in interacting systems

Extends topological characterization to fractional quantum Hall states

Abstract

Hall conductance of noninteracting fermions filling a certain number of Landau levels can be written as a topological invariant. A particular version of this invariant when expressed in terms of the single particle Green's functions directly generalizes to cases when interactions are present including those of fractional Hall states, although in those cases this invariant no longer corresponds to Hall conductance. We argue that when evaluated in fractional Hall states this invariant gives twice the total orbital spin of fermions which in turn is closely related to the Hall viscosity, a quantity characterizing the integer and fractional Hall states which recently received substantial attention in the literature.