Hydrodynamics on the lowest Landau level

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 Streda-type formulas for the equilibrium response to external electric, magnetic and gravitational fields.

References in corpus (8)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Hall Viscosity and Electromagnetic Response
• Towards hydrodynamics without an entropy current
• Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• Parity-Violating Hydrodynamics in 2+1 Dimensions
• Vanishing bulk viscosities and conformal invariance of unitary Fermi gas
• Non-relativistic holography from Horava gravity

Cited by in corpus (6)

• Fractons, dipole symmetries and curved spacetime
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• Warped Conformal Field Theory as Lower Spin Gravity
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Negative magnetoresistivity in chiral fluids and holography
• Galilean Geometry in Condensed Matter Systems