Anisotropic Action of the Strained Quantum Hall System with Tilted Field

We investigate the effective action of an integer quantum Hall system with an in-plane magnetic field subjected to strain fields. We derive the Wen-Zee action, which accounts for both the electromagnetic and viscoelastic responses. The underlying anisotropy generated by the tilted field gives rise to two distinct effective metric tensors stemming from the six-dimensional phase space. The response of the system to strains yields an anisotropic Hall viscosity due to the dependence of the effective metrics on background geometry. The contact terms in the Kubo formula for static strain responses, such as the elastic modulus, can no longer be written in terms of the isotropic compressibility and pressure, but instead has contributions from the two effective metrics. We conclude by applying our analysis to the Boltzmann transport of the semi-classical system.