title: Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains.
abstract: 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.
authors: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors: Hai-Ping
authors: HP
authors: Hu
authors: Center for Interdisciplinary Studies &Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China.
authors: Chen
authors: C
authors: Cheng
authors: 1] Center for Interdisciplinary Studies &Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China [2] Beijing Computational Science Research Center, Beijing 100084, China.
authors: Hong-Gang
authors: HG
authors: Luo
authors: 1] Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China [2] Collaborative Innovation Center of Quantum Matter, Beijing, China.
authors: Shu
authors: S
authors: Chen