### Abstract

Ground-state properties are studied for the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions. The energy, the singlet-triplet energy gap, the two-spin correlation function, and the den Nijs and Rommelse string correlation function in the ground states of finite-size systems of up to 16 spins are calculated exactly. By extrapolating these results, the ground-state properties at the infinite-size limit are discussed. It is found, in particular, that as the ratio of the nnn interaction constant to the nn one increases, the string order parameter (the limiting value of the longest-distance string correlation function) as well as the Haldane gap (the limiting value of the singlet-triplet energy gap) divided by the sum of both interaction constants increases. This result implies that the competition between the antiferromagnetic nn and nnn interactions stabilizes the Haldane phase.

Original language | English |
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Pages (from-to) | 2890-2900 |

Number of pages | 11 |

Journal | Journal of the Physical Society of Japan |

Volume | 61 |

Issue number | 8 |

Publication status | Published - Aug 1992 |

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### Keywords

- Competing interactions
- Ground-state properties
- Haldane gap
- Method of exact diagonalization
- One-dimensional system
- Spin-1 Heisenberg antiferromagnet
- String order parameter

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*61*(8), 2890-2900.