Abstract
Using the recently developed approach to quantum Hall physics based on Newton-Cartan geometry, we consider the hydrodynamics of an interacting system on the lowest Landau level. We rephrase the non-relativistic fluid equations of motion in a manner that manifests the spacetime diffeomorphism invariance of the underlying theory. In the massless (or lowest Landau level) limit, the fluid obeys a force-free constraint which fixes the charge current. An entropy current analysis further constrains the energy response, determining four transverse response functions in terms of only two: an energy magnetization and a thermal Hall conductivity. Kubo formulas are presented for all transport coefficients and constraints from Weyl invariance derived. We also present a number of Středa-type formulas for the equilibrium response to external electric, magnetic and gravitational fields.
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Geracie, M., Son, D.T. Hydrodynamics on the lowest Landau level. J. High Energ. Phys. 2015, 44 (2015). https://doi.org/10.1007/JHEP06(2015)044
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DOI: https://doi.org/10.1007/JHEP06(2015)044