CMSA Quantum Matter in Mathematics and Physics: From Fractional Quantum Hall to higher rank symmetry
Dung Nguyen - Brown University
Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behaviour of FQH systems. Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.