Guiding-center Hall viscosity and intrinsic dipole moment along edges of incompressible fractional quantum Hall fluids

Abstract

The discontinuity of guiding-center Hall viscosity (a bulk property) at edges of incompressible quantum Hall fluids is associated with the presence of an intrinsic electric dipole moment on the edge. If there is a gradient of drift velocity due to a non-uniform electric field, the discontinuity in the induced stress is exactly balanced by the electric force on the dipole. The total Hall viscosity has two distinct contributions: a "trivial" contribution associated with the geometry of the Landau orbits, and a non-trivial contribution associated with guiding-center correlations. We describe a relation between the guiding-center edge-dipole moment and "momentum polarization", which relates the guiding-center part of the bulk Hall viscosity to the "orbital entanglement spectrum(OES)". We observe that using the computationally-more-onerous "real-space entanglement spectrum (RES)" just adds the trivial Landau-orbit contribution to the guiding-center part. This shows that all the non-trivial information is completely contained in the OES, which also exposes a fundamental topological quantity $γ$ = $\tilde c-ν$, the difference between the "chiral stress-energy anomaly" (or signed conformal anomaly) and the chiral charge anomaly. This quantity characterizes correlated fractional quantum Hall fluids, and vanishes in uncorrelated integer quantum Hall fluids.