Hall viscosity of composite fermions

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 [1], we evaluate the Hall viscosities for a large number of fractional quantum Hall states at filling factors of the form ν=n/(2pn±1) [2], where n and p are integers. The calculated Hall viscosities η^A agree with the expression η^A =hSρ/8π, where ρ is the density and S is the ``shift'' in the spherical geometry [3]. We show that the Hall viscosity for ν=n/(2pn+1) may be derived analytically from the microscopic wave functions providing some assumption. This derivation is 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 [4].
[1] S. Pu, Y.-H. Wu, and J. K. Jain, Phys. Rev. B 96, 195302 （2017）
[2] S. Pu, M. Fremling and J. K. Jain, “Hall Viscosity of Composite Fermions”, arXiv: 1910.06496, (2019)
[3] N. Read, Phys. Rev. B 79, 045308 (2009)
[4] J. K. Jain, Phys. Rev. B 40, 8079(R), (1989)