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

2024/10/02 by Nikita Sopenko, Sopenko, Nikita · 4 citations
Physics and Astronomy · #Quantum many-body systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2410.02059

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 ν\bmod 48 ≠ 0 are in a non-trivial invertible phase.

Cited by

• Rényi-like entanglement probe of the chiral central charge
• Probing chiral topological states with permutation defects
• Stacking and the triviality of invertible phases
• Reflection positivity and a refined index for 2d invertible phases

Related

• Reflection positivity and a refined index for 2d invertible phases
• A \mathbb Z₂-index of symmetry protected topological phases with reflection symmetry for quantum spin chains
• A H³(G,\mathbb T)-valued index of symmetry protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems
• 2-d Fermionic SPT with CRT symmetry
• Chiral phases for massive fermions and spinor classifications