Current Developments in Mathematics
Classification of symmetry protected topological phases in quantum spin chains
Pages: 41 – 104
We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems. SPT phases are gapped short-range-entangled quantum phases with a symmetry $G$. We explain that in one and two-dimensional quantum spin systems, there are $H^2(G,U(1))/H^3(G,U(1))$‑valued invariant, confirming a physicists conjecture.
The author was supported in part by the Grants-in-Aid for Scientific Research, JSPS.
Published 30 September 2022