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.
Highlights
Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years
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
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
Summary
Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. 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. 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. We report the findings of a series of non-trivial incommensurate magnetization plateaus as consequence of the existence of large excitation gaps in quasi-periodic quantum spin chains. It is interesting that the spin-flip excitation spectrum of the quasi-periodic Heisenberg model exhibits a butterfly-like structure, which resembles the Hofstadter spectrum of the 2D quantum hall system
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