### Abstract

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully frustrated point, where a localized kink and a freely mobile antikink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. They finally collapse to a local triplet at a sufficient value of the dimerization. The wave function of the bound state, the consequential gap enhancement, and the localization length of the bound state were obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. We also obtained the dispersion relation of the local triplet excitation for the entire phase space. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J_{1}-J_{2} model, or the frustrated ladder model.

Original language | English |
---|---|

Pages (from-to) | 14413-14422 |

Number of pages | 10 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 55 |

Issue number | 21 |

Publication status | Published - 1997 Jun 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*55*(21), 14413-14422.

**Behavior of a frustrated quantum spin chain with bond dimerization.** / Nakamura, Tota; Takada, Satoshi.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 55, no. 21, pp. 14413-14422.

}

TY - JOUR

T1 - Behavior of a frustrated quantum spin chain with bond dimerization

AU - Nakamura, Tota

AU - Takada, Satoshi

PY - 1997/6/1

Y1 - 1997/6/1

N2 - We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully frustrated point, where a localized kink and a freely mobile antikink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. They finally collapse to a local triplet at a sufficient value of the dimerization. The wave function of the bound state, the consequential gap enhancement, and the localization length of the bound state were obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. We also obtained the dispersion relation of the local triplet excitation for the entire phase space. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J1-J2 model, or the frustrated ladder model.

AB - We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully frustrated point, where a localized kink and a freely mobile antikink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. They finally collapse to a local triplet at a sufficient value of the dimerization. The wave function of the bound state, the consequential gap enhancement, and the localization length of the bound state were obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. We also obtained the dispersion relation of the local triplet excitation for the entire phase space. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J1-J2 model, or the frustrated ladder model.

UR - http://www.scopus.com/inward/record.url?scp=0001387503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001387503&partnerID=8YFLogxK

M3 - Article

VL - 55

SP - 14413

EP - 14422

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 21

ER -