### Abstract

The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S=1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents v, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents v, θ and z are estimated to be unity. The exponents v and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent v does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion.

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

Pages (from-to) | 4529-4541 |

Number of pages | 13 |

Journal | Journal of the Physical Society of Japan |

Volume | 63 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1994 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- antiferromagnetic long range order
- critical exponents
- dimerization
- interchain coupling
- quantum Monte Carlo simulation
- spin gap

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Phase Diagram of S=1/2 Quasi-One-Dimensional Heisenberg Model with Dimerized Antiferromagnetic Exchange.** / Katoh, Nobuyuki; Imada, Masatoshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 63, no. 12, pp. 4529-4541. https://doi.org/10.1143/JPSJ.63.4529

}

TY - JOUR

T1 - Phase Diagram of S=1/2 Quasi-One-Dimensional Heisenberg Model with Dimerized Antiferromagnetic Exchange

AU - Katoh, Nobuyuki

AU - Imada, Masatoshi

PY - 1994/1/1

Y1 - 1994/1/1

N2 - The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S=1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents v, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents v, θ and z are estimated to be unity. The exponents v and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent v does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion.

AB - The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S=1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents v, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents v, θ and z are estimated to be unity. The exponents v and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent v does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion.

KW - antiferromagnetic long range order

KW - critical exponents

KW - dimerization

KW - interchain coupling

KW - quantum Monte Carlo simulation

KW - spin gap

UR - http://www.scopus.com/inward/record.url?scp=33646624678&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646624678&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.63.4529

DO - 10.1143/JPSJ.63.4529

M3 - Article

AN - SCOPUS:33646624678

VL - 63

SP - 4529

EP - 4541

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 12

ER -