"Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids

TL;DR

This paper explores the guiding-center Hall viscosity in fractional quantum Hall fluids, revealing its intrinsic metric, relation to incompressibility, and how it distinguishes particle from hole fluids, without requiring rotational symmetry.

Contribution

It introduces a comprehensive characterization of Hall viscosity through an intrinsic metric tensor and establishes bounds related to the structure factor in fractional quantum Hall states.

Findings

Hall viscosity is characterized by a rational number and an intrinsic metric.

The sign of Hall viscosity distinguishes particle and hole fluids.

A lower bound on the structure factor coefficient is established, achieved by conformally-invariant states.

Abstract

The (guiding-center) "Hall viscosity" is a fundamental tensor property of incompressible ``Hall fluids'' exhibiting the fractional quantum Hall effect; it determines the stress induced by a non-uniform electric field, and the intrinsic dipole moment on (unreconstructed) edges. It is characterized by a rational number and an intrinsic metric tensor that defines distances on an ``incompressibility lengthscale''. These properties do not require rotational invariance in the 2D plane. The sign of the guiding-center Hall viscosity distinguishes particle fluids from hole fluids, and its magnitude provides a lower bound to the coefficient of the $O(q^4)$ small-q limit of the guiding center structure factor, a fundamental measure of incompressibility. This bound becomes an equality for conformally-invariant model wavefunctions such as Laughlin or Moore-Read states.