Chiral central charge and the Thermal Hall effect on a lattice

It is well-known that the zero-temperature Hall conductance of a 2d system can be interpreted both as a bulk transport coefficient and a U(1) anomaly for the edge modes. The former interpretation allows one to write down a simple formula for it (Kubo formula). The latter interpretation explains why Hall conductance is a topological invariant. In this talk I will explain the difficulties in extending these considerations to the thermal Hall conductance and how they are overcome. I will argue that the thermal Hall conductance should be regarded as an exact 1-form on the parameter space rather than a function. I will explain how to write-down a Kubo-like formula for this 1-form. Further, I show that the low-temperature thermal Hall conductance of a gapped 2d system is robust under arbitrary deformations which do not close the gap and can be identified with the chiral central charge for the edge modes. This provides the bulk-boundary correspondence for the chiral central charge.

# Condensed Matter Seminar: Anton Kapustin (Caltech) - Chiral central charge and the Thermal Hall effect on a lattice

Event time:

Thursday, September 12, 2019 - 1:00pm to 2:00pm

Location:

Sloane Physics Laboratory (SPL), Room 52

217 Prospect Street

New Haven, CT
06511
Event description: