### Abstract

The ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions are discussed. The ground-state energy, the singlet-triplet energy gap, the Néel correlation function, the dimer correlation function, and the magnetization are calculated exactly for finite-size systems up to 20 spins. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. In particular, it is found that the limiting ground state is in the gapless or finite-gap phase depending on whether 0≦j≦j_{c} or j>j_{c}, where j is the ratio of the second- to the first-neighbor interaction constant and j_{c}=0.30±0.01. Dimer long-range order does exist in the finite-gap phase and it does not in the gapless phase, while no Néel long-range order exists in both phases.

Original language | English |
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Pages (from-to) | 2153-2167 |

Number of pages | 15 |

Journal | Journal of the Physical Society of Japan |

Volume | 56 |

Issue number | 6 |

Publication status | Published - Jun 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*56*(6), 2153-2167.

**Ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with competing interactions.** / Tonegawa, Takashi; Harada, Isao.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 56, no. 6, pp. 2153-2167.

}

TY - JOUR

T1 - Ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with competing interactions

AU - Tonegawa, Takashi

AU - Harada, Isao

PY - 1987/6

Y1 - 1987/6

N2 - The ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions are discussed. The ground-state energy, the singlet-triplet energy gap, the Néel correlation function, the dimer correlation function, and the magnetization are calculated exactly for finite-size systems up to 20 spins. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. In particular, it is found that the limiting ground state is in the gapless or finite-gap phase depending on whether 0≦j≦jc or j>jc, where j is the ratio of the second- to the first-neighbor interaction constant and jc=0.30±0.01. Dimer long-range order does exist in the finite-gap phase and it does not in the gapless phase, while no Néel long-range order exists in both phases.

AB - The ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions are discussed. The ground-state energy, the singlet-triplet energy gap, the Néel correlation function, the dimer correlation function, and the magnetization are calculated exactly for finite-size systems up to 20 spins. By extrapolating these results, the values of the above quantities at the infinite-size limit are estimated. In particular, it is found that the limiting ground state is in the gapless or finite-gap phase depending on whether 0≦j≦jc or j>jc, where j is the ratio of the second- to the first-neighbor interaction constant and jc=0.30±0.01. Dimer long-range order does exist in the finite-gap phase and it does not in the gapless phase, while no Néel long-range order exists in both phases.

UR - http://www.scopus.com/inward/record.url?scp=0012284939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012284939&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012284939

VL - 56

SP - 2153

EP - 2167

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 6

ER -