Topological phases in quasi-periodic spin chains

Teng Xiao, Dizhou Xie, Zhaoli Dong +3 more

Hong‐Chen Jiang, Jiadong Zang, Zheng-Yu Weng +1 more

Yifei Liu, Emil V. Prodan

Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first and higher order Chern numbers. In the present work, we use those findings to generate topological phases at finite magnetization densities that carry first Chern numbers. Given the reduced dimensionality of the spin chains, this provides a unique opportunity to investigate the bulk-boundary correspondence as well as the stability and quantization of the Chern number in the presence of interactions. The later is reformulated using a torus action on the algebra of observables and its quantization and stability is confirmed by numerical simulations. The relations between Chern values and the observed edge spectrum are also discussed.

Antônio Sérgio Teixeira Pires

Henry MullineauxSanders

In the last decade, artificially designed systems have emerged as a promising path to the realisation of topological phases of matter. A particular focus has been on chains of magnetic impurities placed on superconductors which realise mixed dimensional topological phases. To better understand these phases we provide a comprehensive exploration of their topological properties. We demonstrate the challenges of mixed dimensional systems and provide a proof of the conditions of validity of a classification method based on an effective lower-dimensional topological Hamiltonian. The applicability is illustrated through an analytically tractable model of a spiral magnetic interface embedded into a superconductor. We also show that this method provides correct results in regimes where we can demonstrate that other methods proposed for mixed-dimensional models fail. A limitation arises for models with multiple interfaces though, where we find that zeros of Green’s functions can act as false phase boundaries that make the classification by the topological Hamiltonian generally unreliable. Nonetheless, the latter remains applicable for a model of two spiral magnetic interfaces embedded into a superconductor, where in combination with a low-energy effective Hamiltonian, it can probe the local structure of the topological phase. Finally we extend the classification to models with time-periodic and quasi-periodic modulations. We exactly solve a model of a periodically precessing magnetic interface in a superconductor, demonstrating that the driving reduces the superconductor gap. Considering then quasi-periodically evolving magnetic interface, we propose a classification by an extension of the topological Hamiltonian, the topological quasi-energy operator. For a purely one-dimensional model, we provide evidence that quasi-periodic driving tends to destabilise a topological phase. But for a mixed dimensional model, we demonstrate the existence of an enhanced localising potential causing a larger regime of the topological phase.

Haiping Hu, Chen Cheng, Hong‐Gang Luo +1 more

Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems has not been extensively explored due to the failure of direct explanation from the topological band insulator theory on such systems and the origin of the topological property is unclear. Here we report the theoretical discovery of strongly correlated topological states in quasi-periodic Heisenberg spin chain systems corresponding to a series of incommensurate magnetization plateaus under the presence of the magnetic field, which are uniquely determined by the quasi-periodic structure of exchange couplings. The topological features of plateau states are demonstrated by the existence of non-trivial spin-flip edge excitations, which can be well characterized by nonzero topological invariants defined in a two-dimensional parameter space. Furthermore, we demonstrate that the topological invariant of the plateau state can be read out from a generalized Streda formula and the spin-flip excitation spectrum exhibits a similar structure of the Hofstadter's butterfly spectrum for the two-dimensional quantum Hall system on a lattice.