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.

arXiv comment29 pages, 15 figures

References in corpus (9)

• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Valence Bond Solids for Quantum Computation
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• Entanglement in a Valence-Bond-Solid State
• Equal Time Correlations in Haldane Gap Antiferromagnets
• Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
• Onset of incommensurability in quantum spin chains
• Commensurate and incommensurate correlations in Haldane gap antiferromagnets
• Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain

Cited by in corpus (9)

• Transfer Matrices and Excitations with Matrix Product States
• Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
• Topological edge states in spin 1 bilinear-biquadratic model
• Exact ground states for two new spin-1 quantum chains, new features of matrix product states
• Partial Multipartite Entanglement in the Matrix Product State Formalism
• Local dynamics and detection of topology in spin-1 chains
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• Critical phenomena around the SU(3) symmetric tri-critical point of a spin-1 chain
• Cancellation of oscillatory behaviors in incommensurate region