Using the valence-bond-solid (VBS) approach and the Schwinger-boson mean-field approximation, we study the dependence of the Haldane gap of a spin-1 linear-chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter \ensuremath{\Delta} and the constraint factor \ensuremath{\lambda}. As a result, the Haldane gap is reduced by a factor \ensuremath{\sim} ${\mathit{n}}_{\mathit{i}}^{2/3}$ , with ${\mathit{n}}_{\mathit{i}}$ as the impurity concentration, and eventually collapses at ${\mathit{n}}_{\mathit{i}}$ \ensuremath{\sim}1/\ensuremath{\xi} with \ensuremath{\xi} as the VBS correlation length. This theoretical prediction can be verified by neutron-scattering experiments.Using the valence-bond-solid (VBS) approach and the Schwinger-boson mean-field approximation, we study the dependence of the Haldane gap of a spin-1 linear-chain Heisenberg antiferromagnet on impurity doping with different spins. The impurity spins affect the singlet pairing order parameter \ensuremath{\Delta} and the constraint factor \ensuremath{\lambda}. As a result, the Haldane gap is reduced by a factor \ensuremath{\sim}${\mathit{n}}_{\mathit{i}}^{2/3}$, with ${\mathit{n}}_{\mathit{i}}$ as the impurity concentration, and eventually collapses at ${\mathit{n}}_{\mathit{i}}$\ensuremath{\sim}1/\ensuremath{\xi} with \ensuremath{\xi} as the VBS correlation length. This theoretical prediction can be verified by neutron-scattering experiments.

arXiv:cond-mat/9301035Physical review. B, Condensed matterMay 1, 19932 citations

Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain

Kazuo Hida

The ground-state properties of the spin-1/2 Heisenberg chain, which has two exchange couplings (J>J') alternatingly, are studied. This model interpolates the spin-1 antiferromagnetic Heisenberg chain (AFHC) (J'\ensuremath{\rightarrow}-\ensuremath{\infty}, J>0), the dimerized spin-1/2 AFHC (J'\ensuremath{\simeq}J>0), and the uniform spin-1/2 AFHC (J'=J>0) continuously. The string order introduced by den Nijs--Rommelse and Tasaki changes continuously through the Haldane phase and the dimer phase to vanish at J=J'. It is at a maximum for J'=0. This implies that the string order is related to the local singlet correlation in terms of the spin-1/2 model. The lowest excitation can be regarded as the renormalized triplet wave. The reversal of the anisotropy effect on the excitation spectrum of the spin-1 AFHC is also explained in a intuitive way based on this picture.The ground-state properties of the spin-1/2 Heisenberg chain, which has two exchange couplings (J>J') alternatingly, are studied. This model interpolates the spin-1 antiferromagnetic Heisenberg chain (AFHC) (J'\ensuremath{\rightarrow}-\ensuremath{\infty}, J>0), the dimerized spin-1/2 AFHC (J'\ensuremath{\simeq}J>0), and the uniform spin-1/2 AFHC (J'=J>0) continuously. The string order introduced by den Nijs--Rommelse and Tasaki changes continuously through the Haldane phase and the dimer phase to vanish at J=J'. It is at a maximum for J'=0. This implies that the string order is related to the local singlet correlation in terms of the spin-1/2 model. The lowest excitation can be regarded as the renormalized triplet wave. The reversal of the anisotropy effect on the excitation spectrum of the spin-1 AFHC is also explained in a intuitive way based on this picture.

Physical review. B, Condensed matterFeb 1, 1992274 citations

Haldane Gap in the Spin-1/2 Double Chain Heisenberg Antiferromagnet -Numerical Diagonalization and Projector Monte Carlo Study-

Kazuo Hida

The properties of the spin-1/2 double chain Heisenberg antiferromagnet are studied by means of the numerical diagonalization and the projector Monte Carlo simulation. The model consists of the two spin 1/2 antiferromagnetic quantum Heisenberg chains coupled with each other via the ferromagnetic interchain coupling J ′ . It is shown that the first excited state has a gap for large enough J ′ . This gap continues to the Haldane gap in the limit J ′ →∞, where spins on the different chains form triplets on each site. On the other hand, the gap decreases rapidly between J ′ =1.0 and 0.6 and is undetectable for J ′ <0.6 within the present accuracy.The properties of the spin-1/2 double chain Heisenberg antiferromagnet are studied by means of the numerical diagonalization and the projector Monte Carlo simulation. The model consists of the two spin 1/2 antiferromagnetic quantum Heisenberg chains coupled with each other via the ferromagnetic interchain coupling J ′ . It is shown that the first excited state has a gap for large enough J ′ . This gap continues to the Haldane gap in the limit J ′ →∞, where spins on the different chains form triplets on each site. On the other hand, the gap decreases rapidly between J ′ =1.0 and 0.6 and is undetectable for J ′ <0.6 within the present accuracy.

Journal of the Physical Society of JapanApr 15, 199178 citations

Haldane gap in S = 2 XXZ quantum antiferromagnet

Charudatt Kadolkar, Neena Goveas, Dipan K. Ghosh +1 more

Journal of Magnetism and Magnetic MaterialsJan 1, 19981 citation

{\mathit{n}}_{\mathit{i}}^{2/3}

, with

{\mathit{n}}_{\mathit{i}}

as the impurity concentration, and eventually collapses at

{\mathit{n}}_{\mathit{i}}

\ensuremath{\sim}1/\ensuremath{\xi} with \ensuremath{\xi} as the VBS correlation length. This theoretical prediction can be verified by neutron-scattering experiments.