Guiding-center Hall viscosity and intrinsic dipole moment of fractional quantum Hall states

Abstract

The fractional quantum Hall effect (FQHE) is the archetype of the strongly correlated systems and the topologically ordered phases. Unlike the integer quantum Hall effect (IQHE) which can be explained by single-particle physics, FQHE exhibits many emergent properties that are due to the strong correlation among many electrons. In this Thesis, among those emergent properties of FQHE, we focus on the guiding-center metric, the guiding-center Hall viscosity, the guiding-center spin, the intrinsic electric dipole moment and the orbital entanglement spectrum.

Specifically, we show that 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.

We show that 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 intrinsic dipole moment and ``momentum polarization'', which relates the guiding-center Hall viscosity to the ``orbital entanglement spectrum(OES)''.

We observe that using the computationally-more-onerous ``real-space entanglement spectrum (RES)'' in the momentum polarization calculation 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 $\gamma$ = $\tilde c-\nu$, 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 integer quantum Hall fluids which are uncorrelated.