### Abstract

The ground state of the bond-random antiferromagnetic S = 1 Heisenberg chain with the biquadratic interaction -β∑_{i}(S_{i} · S_{i+1})^{2} is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase β ≈ 0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremely broad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.

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

Pages (from-to) | 35-47 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 252 |

Issue number | 1-2 |

Publication status | Published - Apr 1 1998 |

### Fingerprint

### Keywords

- Bond randomness
- Exact-diagonalization method
- Haldane phase
- Random-singlet phase

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**Numerical analysis of the bond-random antiferromagnetic S = 1 Heisenberg chain.** / Nishiyama, Yoshihiro.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 252, no. 1-2, pp. 35-47.

}

TY - JOUR

T1 - Numerical analysis of the bond-random antiferromagnetic S = 1 Heisenberg chain

AU - Nishiyama, Yoshihiro

PY - 1998/4/1

Y1 - 1998/4/1

N2 - The ground state of the bond-random antiferromagnetic S = 1 Heisenberg chain with the biquadratic interaction -β∑i(Si · Si+1)2 is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase β ≈ 0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremely broad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.

AB - The ground state of the bond-random antiferromagnetic S = 1 Heisenberg chain with the biquadratic interaction -β∑i(Si · Si+1)2 is investigated by means of the exact-diagonalization method and the finite-size-scaling analysis. It is shown that the Haldane phase β ≈ 0 persists against the randomness; namely, no randomness-driven phase transition is observed until at a point of extremely broad-bond distribution. We found that in the Haldane phase, the magnetic correlation length is kept hardly changed. These results are contrastive to those of an analytic theory which predicts a second-order phase transition between the Haldane and the random-singlet phases at a certain critical randomness.

KW - Bond randomness

KW - Exact-diagonalization method

KW - Haldane phase

KW - Random-singlet phase

UR - http://www.scopus.com/inward/record.url?scp=0346907965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346907965&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346907965

VL - 252

SP - 35

EP - 47

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-2

ER -