Skip to main content
Browse by:
GROUP

Effective March 10, 2020, all Duke-sponsored events over 50 people have been cancelled, rescheduled, postponed or virtualized.
Please check with the event contact regarding event status. For more information, please see https://coronavirus.duke.edu/events

Condensed Matter Seminar "Integers in gapped quantum lattice systems"

Event Image
Icon calendar
Friday, April 05, 2019
Icon time
1:00 pm - 2:00 pm
Icon speaker
Martin Fraas (Virginia Tech)
Icon series
Condensed Matter Seminar

We propose an index for gapped quantum lattice systems that conserve a U(1)-charge. This index takes integer values and it is therefore stable under perturbations. Our formulation is general, but we show that the index reduces to (i) an index of projections in the non-interacting case, (ii) the filling factor for translational invariant systems, (iii) the quantum Hall conductance in the two-dimensional setting without any additional symmetry. Example (ii) recovers the Lieb-Schultz-Mattis theorem, (iii) provides a new and short proof of quantization of Hall conductance in interacting many-body systems. Additionally, we show Avron-Dana-Zak relations for both integer and fractional quantum Hall effect.

Contact: Cristin Paul