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.
Highlights
Density-curvature response and the chiral central charge [13]
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
This construction of the hydrodynamic theory is simplest in relativistic physics, where covariance is manifest in the equations of motion
Summary
We begin with a brief recap of recent work on the Ward identities of non-relativistic systems. The above is a covariant generalization of these equations to arbitrary backgrounds, subjected to a LLL projection in the form of a massless limit These identities assume a spinful fluid of spin s = 1. Before the LLL projection the equation for stress conservation contains terms involving the momentum current These drop out upon taking the massless limit m → 0 and stress conservation becomes the force balance (2.5). Note in all cases the divergence operator takes the form ∇μ − Gμ where Gμ = T ννμ which is the correct form of the divergence on a torsionful manifold In writing these formulas, we have chosen g-factor g = 2 and spin s = 1 as we are always free to do. A given system may not satisfy these conditions, but in ref. [17] we present a precise dictionary that allows one to translate our results to the general case
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