### Abstract

The ground state energy, the energy gap and the Fourier transform of the staggered spin correlation function S(Q) at zero temperature are investigated for the 5=1/2 antiferromagnetic Heisenberg model on a dimerized square lattice with the help of the spin-wave approximations, the second-order perturbation expansion and the quantum Monte Carlo simulations. In contrast to one-dimensional case, the spin gap appears above a finite critical value of the dimerization parameter. Sc - 0.303, where the second-order transition takes place. The antiferromagnetic long range order exists below Sc. The critical exponent of the order parameter in the antiferromagnetically ordered state is estimated by quantum Monte Carlo calculation to be -{dc∼- with B=0.27 ±0.04, while the correlation length in the spin gap region is scaled as - (S-Sc)v with v= 1.36±0.05. All of them are different from the estimates in one-dimension, v=l and the spin-wave approximation, fi=v=l. Possible relevance of our result for the spin gap behavior in high-Tc superconductors is also discussed.

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

Pages (from-to) | 3728-3740 |

Number of pages | 13 |

Journal | Journal of the Physical Society of Japan |

Volume | 62 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1993 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Phase Diagram of S= 1/2 Antiferromagnetic Heisenberg Model on a Dimerized Square Lattice.** / Katoh, Nobuyuki; Imada, Masatoshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 62, no. 10, pp. 3728-3740. https://doi.org/10.1143/JPSJ.62.3728

}

TY - JOUR

T1 - Phase Diagram of S= 1/2 Antiferromagnetic Heisenberg Model on a Dimerized Square Lattice

AU - Katoh, Nobuyuki

AU - Imada, Masatoshi

PY - 1993/1/1

Y1 - 1993/1/1

N2 - The ground state energy, the energy gap and the Fourier transform of the staggered spin correlation function S(Q) at zero temperature are investigated for the 5=1/2 antiferromagnetic Heisenberg model on a dimerized square lattice with the help of the spin-wave approximations, the second-order perturbation expansion and the quantum Monte Carlo simulations. In contrast to one-dimensional case, the spin gap appears above a finite critical value of the dimerization parameter. Sc - 0.303, where the second-order transition takes place. The antiferromagnetic long range order exists below Sc. The critical exponent of the order parameter in the antiferromagnetically ordered state is estimated by quantum Monte Carlo calculation to be -{dc∼- with B=0.27 ±0.04, while the correlation length in the spin gap region is scaled as - (S-Sc)v with v= 1.36±0.05. All of them are different from the estimates in one-dimension, v=l and the spin-wave approximation, fi=v=l. Possible relevance of our result for the spin gap behavior in high-Tc superconductors is also discussed.

AB - The ground state energy, the energy gap and the Fourier transform of the staggered spin correlation function S(Q) at zero temperature are investigated for the 5=1/2 antiferromagnetic Heisenberg model on a dimerized square lattice with the help of the spin-wave approximations, the second-order perturbation expansion and the quantum Monte Carlo simulations. In contrast to one-dimensional case, the spin gap appears above a finite critical value of the dimerization parameter. Sc - 0.303, where the second-order transition takes place. The antiferromagnetic long range order exists below Sc. The critical exponent of the order parameter in the antiferromagnetically ordered state is estimated by quantum Monte Carlo calculation to be -{dc∼- with B=0.27 ±0.04, while the correlation length in the spin gap region is scaled as - (S-Sc)v with v= 1.36±0.05. All of them are different from the estimates in one-dimension, v=l and the spin-wave approximation, fi=v=l. Possible relevance of our result for the spin gap behavior in high-Tc superconductors is also discussed.

KW - antiferromagnetic long range order

KW - critical exponents

KW - dimerization

KW - quantum Monte Carlo simulation

KW - spin gap

UR - http://www.scopus.com/inward/record.url?scp=21344487468&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344487468&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.62.3728

DO - 10.1143/JPSJ.62.3728

M3 - Article

AN - SCOPUS:21344487468

VL - 62

SP - 3728

EP - 3740

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 10

ER -