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arXiv:1511.06671 · Physical review. B./Physical review. B

Fractional topological states in quantum spin chains with periodical modulation

Haiping Hu, Huaiming Guo, Shu Chen

Published Apr 18, 2016• 10 citations
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Abstract

We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically nontrivial degenerate ground states at some specific magnetizations, which can be characterized by the nonzero-integer total Chern numbers of the degenerate ground states and the emergence of nontrivial edge states under open boundary conditions. We find that the low-energy excitations obey bosonic $\ensuremath{\nu}=1/2$ fractional statistics for the spin-$1/2$ system and $\ensuremath{\nu}=1$ non-Abelian statistics for the spin-1 system, respectively. The discovered fractional quantum states provide another route to the theoretical exploration of fractional quantum states in correlated spin systems.

DOI
10.1103/physrevb.93.155133

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We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.
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