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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.

Zoom: https://harvard.zoom.us/j/977347126

Condensed-matter theorists have discovered examples of physical systems with unusual behavior, such as pointlike excitations that behave neither as bosons nor as fermions, leading to the idea of topological phases of matter. Classifying the possible topological phases has been the focus of a lot of research in the last decade in condensed-matter theory and nearby areas of mathematics. In this talk, I’ll focus primarily on the special case of invertible phases, also called symmetry-protected topological (SPT) phases, whose classification uses techniques from homotopy theory. I will discuss two different approaches to this, due to Kitaev and Freed-Hopkins, followed by details of the homotopy-theoretic classifications. The latter includes work of Freed-Hopkins and of myself.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones.

References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx] Jing-Yuan Chen, [1902.06756].

Zoom: https://harvard.zoom.us/j/977347126