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- 24 when the effective conformal field theory description is valid. Using this index, we prove that free fermionic systems with Chern number 48 ≠ 0 are in a non-trivial invertible phase.
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