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

• URL: http://arxiv.org/abs/2410.02059v1
• Date: Wed, 2 Oct 2024 22:11:22 GMT
• Title: An index for invertible phases of two-dimensional quantum spin systems
• Authors: Nikita Sopenko,
• Abstract summary: We prove that free fermionic systems with Chern number $nu bmod 48 neq 0$ are in a non-trivial invertible phase.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $c_- \bmod 24$ when the effective conformal field theory description is valid. Using this index, we prove that free fermionic systems with Chern number $\nu \bmod 48 \neq 0$ are in a non-trivial invertible phase.

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