Physics (Internal)

"Polarization, Large Gauge Invariance, and Quantum Hall Effect on Lattice"

This event is part of the Condensed Matter Theory Seminar Series.

Quantum systems on a non-simply connected space possess a "large" gauge invariance. Laughlin utilized this to explain quantum Hall effect. Later, it was applied to elucidate a universal relation between filling factor and energy spectrum in quantum many-body systems on periodic lattices (Lieb-Schultz-Mattis-M.O.-Hastings). Somewhat surprisingly, the large gauge invariance is also deeply related to modern theory of electric polarization developed by Resta et al. Combining these ideas together, we can derive a constraint on the Hall conductivity of a many-particle system on a periodic lattice, with a given magnetic flux per plaquette and particle density.