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Incommensurability and edge states in the one-dimensional S=1 bilinear-biquadratic model

Takahiro Murashima·Kiyohide Nomura
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Abstract

Commensurate-incommensurate change on the one-dimensional S=1 bilinear-biquadratic model (${\cal H}(α)=\sum_i \{{\bf S}_i\cdot {\bf S}_{i+1} +α({\bf S}_i\cdot{\bf S}_{i+1})^2\}$) is examined. The gapped Haldane phase has two subphases (the commensurate Haldane subphase and the incommensurate Haldane subphase) and the commensurate-incommensurate change point (the Affleck-Kennedy-Lieb-Tasaki point, $α=1/3$). There have been two different analytical predictions about the static structure factor in the neighborhood of this point. By using the Sørensen-Affleck prescription, these static structure factors are related to the Green functions, and also to the energy gap behaviors. Numerical calculations support one of the predictions. Accordingly, the commensurate-incommensurate change is recognized as a motion of a pair of poles in the complex plane.

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Takahiro Murashima, Kiyohide Nomura. 2006-05-02. Incommensurability and edge states in the one-dimensional S=1 bilinear-biquadratic model. https://doi.org/10.1103/physrevb.73.214431

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