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 the 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 nonuniform 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 nontrivial 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'' just adds the trivial Landau-orbit contribution to the guiding-center part. This shows that all the nontrivial information is completely contained in the OES, which also exposes a fundamental topological quantity, $\ensuremath{\gamma}$ = $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{c}\ensuremath{-}\ensuremath{\nu}$, 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.