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

Abstract

Commensurate-incommensurate change on the one-dimensional S=1 bilinear-biquadratic model ($\mathcal{H}(\alpha )={\sum }_i\{{\mathbf{S}}_i\cdot {\mathbf{S}}_{i+1}+\alpha ({\mathbf{S}}_i\cdot {\mathbf{S}}_{i+1}{)}^2\}$) 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, $\alpha =1/3$). 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.

29 pages, 15 figures

References in corpus (2)

• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Valence Bond Solids for Quantum Computation

Cited by in corpus (5)

• Transfer Matrices and Excitations with Matrix Product States
• Local dynamics and detection of topology in spin-1 chains
• Critical phenomena around the SU(3) symmetric tri-critical point of a spin-1 chain
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• Cancellation of oscillatory behaviors in incommensurate region