An index for invertible phases of two-dimensional quantum spin systems

Abstract

We define an index for invertible phases of two-dimensional fermionic and bosonic quantum spin systems without any additional symmetry. Conjecturally, it provides a microscopic definition of an invariant related to the chiral central charge of the boundary modes $c_{-}\mathrm{mod}24$ when the effective conformal field theory description is valid. Using this index, we prove that free fermionic systems with Chern number $\nu \mathrm{mod}48\ne 0$ are in a non-trivial invertible phase.

arXiv comment21 pages, 6 figures