Topological phases in quasi-periodic spin chains

In [Y. Liu et al., arXiv:2009.03752], we investigate topological phases in quasi-periodic spin-chain models and their bulk-boundary principles by numerical and K-theoretic methods. In the uncorrelated case with magnetization M=1,2, and 3, the observed chiral bands indicate that the spectral gaps are topological and K-theoretic labels enable us to match the first Chern number with the numbers of topological edge modes. When the interaction is introduced, the robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. The bulk-boundary correspondence of the interacting model is studied in [Y. Liu et al., arXiv:2010.06171]. In this work, we generate topological phases at finite magnetization densities that carry the first Chern numbers. We conclude that the non-degenerate character of a ground state carrying a non-trivial Chern number is destroyed when open boundary conditions are used. Based on those findings, we are able to generate high throughput of topological correlated states at finite densities.