Hall Viscosity of Composite Fermions

TL;DR

This paper calculates the Hall viscosity for various fractional quantum Hall states using composite fermion wave functions, confirming a universal relation with the state’s shift and discussing underlying symmetries and derivations.

Contribution

It provides explicit calculations of Hall viscosity for a broad class of fractional quantum Hall states using a recent composite fermion theory formulation.

Findings

Hall viscosities agree with the universal formula involving the shift and density.

Analytic derivation of Hall viscosity for certain states from microscopic wave functions.

Discussion of modular invariance and Landau level projection effects.

Abstract

Hall viscosity, also known as the Lorentz shear modulus, has been proposed as a topological property of a quantum Hall fluid. Using a recent formulation of the composite fermion theory on the torus, we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form $\nu=n/(2pn\pm 1)$, where $n$ and $p$ are integers, from the explicit wave functions for these states. The calculated Hall viscosities $\eta^A$ agree with the expression $\eta^A=(\hbar/4) {\cal S}\rho$, where $\rho$ is the density and ${\cal S}=2p\pm n$ is the "shift" in the spherical geometry. We discuss the role of modular invariance of the wave functions, of the center-of-mass momentum, and also of the lowest-Landau-level projection. Finally, we show that the Hall viscosity for $\nu={n\over 2pn+1}$ may be derived analytically from the microscopic wave functions, provided that the overall normalization factor satisfies a certain behavior in the thermodynamic limit. This derivation should be applicable to a class of states in the parton construction, which are products of integer quantum Hall states with magnetic fields pointing in the same direction.