International Journal of Modern Physics C

HEISENBERG ANTIFERROMAGNETIC CHAIN of SPIN S=1

O. Golinelli, Th. Jolicœur, R. Lacaze

Published Apr 1, 1994• 0 citations

Abstract

The Heisenberg antiferromagnetic chain of spin 1 with the most general single ion anisotropy is numerically analyzed. Chains of length up to 22 sites are studied by a Lanczös method and up to 32 sites with a quantum Monte Carlo. Gaps, magnetic excitations, dynamical properties and magnetic field behaviour are obtained. The recent neutron scattering experiments on the quasi one-dimensional antiferromagnet NENP are fully explained by our results.

DOI: 10.1142/s0129183194000271

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International Journal of Modern Physics C

HEISENBERG ANTIFERROMAGNETIC CHAIN of SPIN S=1

O. Golinelli, Th. Jolicœur, R. Lacaze

Published Apr 1, 1994• 0 citations

Publisher

Abstract

DOI: 10.1142/s0129183194000271

Related papers

Haldane gaps in a spin-1 Heisenberg chain with easy-plane single-ion anisotropy

O. Golinelli, Th. Jolicœur, R. Lacaze

We study a Heisenberg antiferromagnetic chain of spin S=1 with nearest-neighbor exchange interaction J and easy-plane single-ion anisotropy D. We follow the splitting of the Haldane gap into two components as a function of the anisotropy. Chains of length up to 16 sites are studied by a Lancz\"os method and longer chains up to 32 sites have been investigated by a quantum Monte Carlo simulation for D/J=0.10, 0.15, 0.20, and 0.25. A careful finite-size scaling treatment of our data leads to values that are directly relevant to the interpretation of experiments on Ni( ${\mathrm{C}}_{2}$ ${\mathrm{H}}_{8}$ ${\mathrm{N}}_{2}$ ${)}_{2}$ ${\mathrm{NO}}_{2}$ ${\mathrm{ClO}}_{4}$ (NENP). We discuss the relationship between our results and the magnetic-susceptibility measurements as well as the inelastic-neutron-scattering data and on the Haldane conjecture. Values are proposed for the parameters D and J in the case of NENP.We study a Heisenberg antiferromagnetic chain of spin S=1 with nearest-neighbor exchange interaction J and easy-plane single-ion anisotropy D. We follow the splitting of the Haldane gap into two components as a function of the anisotropy. Chains of length up to 16 sites are studied by a Lancz\"os method and longer chains up to 32 sites have been investigated by a quantum Monte Carlo simulation for D/J=0.10, 0.15, 0.20, and 0.25. A careful finite-size scaling treatment of our data leads to values that are directly relevant to the interpretation of experiments on Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$${\mathrm{ClO}}_{4}$ (NENP). We discuss the relationship between our results and the magnetic-susceptibility measurements as well as the inelastic-neutron-scattering data and on the Haldane conjecture. Values are proposed for the parameters D and J in the case of NENP.

Physical review. B, Condensed matterMay 1, 199297 citations

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We study the dispersion of magnetic excitations in a Heisenberg antiferromagnetic chain of spin S=1 with exchange J and single-ion anisotropy D. Chains of length up to 18 sites are studied by a Lanczo\ifmmode\ddot\else\textasciidieresis\fi{}s method. For the Haldane phase D ${\mathit{D}}_{\mathit{c}}$ \ensuremath{\approxeq}J we show that the gap at zero momentum and ${\mathit{S}}^{\mathit{z}}$ =1 is given by the sum of the gaps in the sectors ${\mathit{S}}^{\mathit{z}}$ =1 and ${\mathit{S}}^{\mathit{z}}$ =0 at momentum \ensuremath{\pi}. The transition region near D=J is likely to be reduced to an isolated point. Large-D perturbation theory is smoothly recovered as soon as D>2J. We discuss the implications for experiments on Ni( ${\mathrm{C}}_{2}$ ${\mathrm{H}}_{8}$ ${\mathrm{N}}_{2}$ ${)}_{2}$ ${\mathrm{NO}}_{2}$ ${\mathrm{ClO}}_{4}$ (NENP) as well as ${\mathrm{CsFeBr}}_{3}$ .We study the dispersion of magnetic excitations in a Heisenberg antiferromagnetic chain of spin S=1 with exchange J and single-ion anisotropy D. Chains of length up to 18 sites are studied by a Lanczo\ifmmode\ddot\else\textasciidieresis\fi{}s method. For the Haldane phase D${\mathit{D}}_{\mathit{c}}$\ensuremath{\approxeq}J we show that the gap at zero momentum and ${\mathit{S}}^{\mathit{z}}$=1 is given by the sum of the gaps in the sectors ${\mathit{S}}^{\mathit{z}}$=1 and ${\mathit{S}}^{\mathit{z}}$=0 at momentum \ensuremath{\pi}. The transition region near D=J is likely to be reduced to an isolated point. Large-D perturbation theory is smoothly recovered as soon as D>2J. We discuss the implications for experiments on Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$${\mathrm{ClO}}_{4}$ (NENP) as well as ${\mathrm{CsFeBr}}_{3}$.

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Elementary excitations of an anisotropic spin-1 chain

Minoru Takahashi

The neutron-scattering intensity and energy eigenvalues of the elementary excitations of the S=1 antiferromagnetic Heisenberg chain with single-ion anisotropy [scrH=J ${\mathit{tsum}}_{\mathit{i}=1}^{\mathit{N}}$ ${\mathbf{S}}_{\mathit{i}}$ \ensuremath{\cdot} ${\mathbf{S}}_{\mathit{i}+1}$ +D tsum( ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ ${)}^{2}$ ] are calculated with a numerical diagonalization method and a projector Monte Carlo method. We set D/J=0.2,0.0,-0.2 and N=14,16,18,32. For D\ensuremath{\ne}0, the elementary excitations in the subspace of ${\mathit{S}}^{\mathit{z}}$ =\ifmmode\pm\else\textpm\fi{}1 and in the subspace of ${\mathit{S}}^{\mathit{z}}$ =0 are different. The ${\mathit{S}}^{\mathit{z}}$ =\ifmmode\pm\else\textpm\fi{}1 branch is lower than the ${\mathit{S}}^{\mathit{z}}$ =0 branch near Q=\ensuremath{\pi}; however, it becomes slightly higher in other regions. The crossing of levels occurs at Q\ensuremath{\simeq}\ifmmode\pm\else\textpm\fi{}0.7\ensuremath{\pi}. We find that the low-lying excited state has a weight of more than 90% in the dynamical structure factor, except for Q\ensuremath{\simeq}0. Our results explain recent experimental results on Ni( ${\mathrm{C}}_{2}$ ${\mathrm{H}}_{8}$ ${\mathrm{N}}_{2}$ ${)}_{2}$ ${\mathrm{NO}}_{2}$ ${\mathrm{ClO}}_{4}$ .The neutron-scattering intensity and energy eigenvalues of the elementary excitations of the S=1 antiferromagnetic Heisenberg chain with single-ion anisotropy [scrH=J ${\mathit{tsum}}_{\mathit{i}=1}^{\mathit{N}}$ ${\mathbf{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathbf{S}}_{\mathit{i}+1}$+D tsum(${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${)}^{2}$] are calculated with a numerical diagonalization method and a projector Monte Carlo method. We set D/J=0.2,0.0,-0.2 and N=14,16,18,32. For D\ensuremath{\ne}0, the elementary excitations in the subspace of ${\mathit{S}}^{\mathit{z}}$=\ifmmode\pm\else\textpm\fi{}1 and in the subspace of ${\mathit{S}}^{\mathit{z}}$=0 are different. The ${\mathit{S}}^{\mathit{z}}$=\ifmmode\pm\else\textpm\fi{}1 branch is lower than the ${\mathit{S}}^{\mathit{z}}$=0 branch near Q=\ensuremath{\pi}; however, it becomes slightly higher in other regions. The crossing of levels occurs at Q\ensuremath{\simeq}\ifmmode\pm\else\textpm\fi{}0.7\ensuremath{\pi}. We find that the low-lying excited state has a weight of more than 90% in the dynamical structure factor, except for Q\ensuremath{\simeq}0. Our results explain recent experimental results on Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$${\mathrm{ClO}}_{4}$.

Physical review. B, Condensed matterJul 1, 199351 citations

Field-theory treatment of the Heisenberg spin-1 chain

Alexei M. Tsvelik

We suggest a new field-theory treatment of the Heisenberg spin-1 chain with a single-ion anisotropy as a theory of three Majorana (real) fermions. We calculate the static and dynamic magnetic susceptibilities. We show that our results are in a good agreement with the experimental data for NENP [Ni( ${\mathrm{C}}_{2}$ ${\mathrm{H}}_{8}$ ${\mathrm{N}}_{2}$ ) ${\mathrm{NO}}_{2}$ ${\mathrm{ClO}}_{4}$ ] compound. In particular, we eliminate the reported contradiction between excitation gaps deduced from high-field magnetization measurements and neutron scattering.We suggest a new field-theory treatment of the Heisenberg spin-1 chain with a single-ion anisotropy as a theory of three Majorana (real) fermions. We calculate the static and dynamic magnetic susceptibilities. We show that our results are in a good agreement with the experimental data for NENP [Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$)${\mathrm{NO}}_{2}$${\mathrm{ClO}}_{4}$] compound. In particular, we eliminate the reported contradiction between excitation gaps deduced from high-field magnetization measurements and neutron scattering.

Physical review. B, Condensed matterDec 1, 1990151 citations

{\mathrm{C}}_{2}

{\mathrm{H}}_{8}

{\mathrm{N}}_{2}

{)}_{2}

{\mathrm{NO}}_{2}

{\mathrm{ClO}}_{4}

(NENP). We discuss the relationship between our results and the magnetic-susceptibility measurements as well as the inelastic-neutron-scattering data and on the Haldane conjecture. Values are proposed for the parameters D and J in the case of NENP.

{\mathit{D}}_{\mathit{c}}

\ensuremath{\approxeq}J we show that the gap at zero momentum and

{\mathit{S}}^{\mathit{z}}

=1 is given by the sum of the gaps in the sectors

{\mathit{S}}^{\mathit{z}}

=1 and

{\mathit{S}}^{\mathit{z}}

=0 at momentum \ensuremath{\pi}. The transition region near D=J is likely to be reduced to an isolated point. Large-D perturbation theory is smoothly recovered as soon as D>2J. We discuss the implications for experiments on Ni(

{\mathrm{C}}_{2}

{\mathrm{H}}_{8}

{\mathrm{N}}_{2}

{)}_{2}

{\mathrm{NO}}_{2}

{\mathrm{ClO}}_{4}

(NENP) as well as

{\mathrm{CsFeBr}}_{3}

The neutron-scattering intensity and energy eigenvalues of the elementary excitations of the S=1 antiferromagnetic Heisenberg chain with single-ion anisotropy [scrH=J

{\mathit{tsum}}_{\mathit{i}=1}^{\mathit{N}}

{\mathbf{S}}_{\mathit{i}}

\ensuremath{\cdot}

{\mathbf{S}}_{\mathit{i}+1}

+D tsum(

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

{)}^{2}

] are calculated with a numerical diagonalization method and a projector Monte Carlo method. We set D/J=0.2,0.0,-0.2 and N=14,16,18,32. For D\ensuremath{\ne}0, the elementary excitations in the subspace of

{\mathit{S}}^{\mathit{z}}

=\ifmmode\pm\else\textpm\fi{}1 and in the subspace of

{\mathit{S}}^{\mathit{z}}

=0 are different. The

{\mathit{S}}^{\mathit{z}}

=\ifmmode\pm\else\textpm\fi{}1 branch is lower than the

{\mathit{S}}^{\mathit{z}}

=0 branch near Q=\ensuremath{\pi}; however, it becomes slightly higher in other regions. The crossing of levels occurs at Q\ensuremath{\simeq}\ifmmode\pm\else\textpm\fi{}0.7\ensuremath{\pi}. We find that the low-lying excited state has a weight of more than 90% in the dynamical structure factor, except for Q\ensuremath{\simeq}0. Our results explain recent experimental results on Ni(

{\mathrm{C}}_{2}

{\mathrm{H}}_{8}

{\mathrm{N}}_{2}

{)}_{2}

{\mathrm{NO}}_{2}

{\mathrm{ClO}}_{4}

{\mathrm{C}}_{2}

{\mathrm{H}}_{8}

{\mathrm{N}}_{2}

)

{\mathrm{NO}}_{2}

{\mathrm{ClO}}_{4}

] compound. In particular, we eliminate the reported contradiction between excitation gaps deduced from high-field magnetization measurements and neutron scattering.