Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains

TL;DR

This paper theoretically uncovers topologically nontrivial states in quasi-periodic quantum spin chains, revealing incommensurate magnetization plateaus with edge excitations and topological invariants, expanding understanding beyond band insulators.

Contribution

It introduces a new class of strongly correlated topological states in quasi-periodic spin chains, characterized by non-trivial edge excitations and topological invariants, linked to incommensurate magnetization plateaus.

Findings

Discovery of topological incommensurate magnetization plateaus.

Existence of non-trivial spin-flip edge excitations.

Topological invariants characterized by a generalized Streda formula.

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.