Physical review. B, Condensed matter

Field-theory treatment of the Heisenberg spin-1 chain

Alexei M. Tsvelik

Published Dec 1, 1990• 151 citations

Abstract

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.

DOI: 10.1103/physrevb.42.10499

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Novel treatment of the Heisenberg spin-1 chain: Application to Ni(C2H8N2)2NO2(ClO4)α

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Elementary excitations of an anisotropic spin-1 chain

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HEISENBERG ANTIFERROMAGNETIC CHAIN of SPIN S=1

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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.

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Physical review. B, Condensed matterMay 1, 199297 citations

Physical review. B, Condensed matter

Field-theory treatment of the Heisenberg spin-1 chain

Alexei M. Tsvelik

Published Dec 1, 1990• 151 citations

Publisher

Abstract

{\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.

DOI: 10.1103/physrevb.42.10499

Related papers

Novel treatment of the Heisenberg spin-1 chain: Application to Ni(C2H8N2)2NO2(ClO4)α

Alexei M. Tsvelik

AIP conference proceedingsJan 1, 19900 citations

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

HEISENBERG ANTIFERROMAGNETIC CHAIN of SPIN S=1

O. Golinelli, Th. Jolicœur, R. Lacaze

International Journal of Modern Physics CApr 1, 19940 citations

A Quantum Spin Chain in High Magnetic Fields

K. Katsumata, H. Hori, Tetsuya Takeuchi +4 more

The magnetization process of a single crystal of the spin (S) one linear-chain Heisenberg antiferromagnet, Ni(C2H8N2)2NO2(ClO4), under very high magnetic field has been measured. The magnetization is very small in the low-field region and begins to increase sharply at a finite field for all three of the principal axes. The transition field (HT) above which the system becomes magnetic depends on the direction of the applied field. These experimental results are consistent with the picture that (i) the ground state of S=1 linear chain Heisenberg antiferromagnet is a singlet and (ii) the system becomes magnetic above HT due to closing of the quantum energy gap. The experimental results are analyzed based on a simple energy level scheme. The anisotropy in HT is successfully explained by the theory using the following parameters; the Haldane gap energy EG=17K and the single ion anisotropy constant |D|=16K. These values of EG and D are close to those obtained from other experiments. Using the theory developed in analyzing the magnetization data, we can also explain the behavior of the excitation spectrum of this compound in external magnetic fields determined from the neutron inelastic scattering experiment.The magnetization process of a single crystal of the spin (S) one linear-chain Heisenberg antiferromagnet, Ni(C2H8N2)2NO2(ClO4), under very high magnetic field has been measured. The magnetization is very small in the low-field region and begins to increase sharply at a finite field for all three of the principal axes. The transition field (HT) above which the system becomes magnetic depends on the direction of the applied field. These experimental results are consistent with the picture that (i) the ground state of S=1 linear chain Heisenberg antiferromagnet is a singlet and (ii) the system becomes magnetic above HT due to closing of the quantum energy gap. The experimental results are analyzed based on a simple energy level scheme. The anisotropy in HT is successfully explained by the theory using the following parameters; the Haldane gap energy EG=17K and the single ion anisotropy constant |D|=16K. These values of EG and D are close to those obtained from other experiments. Using the theory developed in analyzing the magnetization data, we can also explain the behavior of the excitation spectrum of this compound in external magnetic fields determined from the neutron inelastic scattering experiment.

Progress of Theoretical Physics SupplementMay 16, 20130 citations

Dispersion of magnetic excitations in a spin-1 chain with easy-plane anisotropy

O. Golinelli, Th. Jolicœur, R. Lacaze

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 ${\mathrm{CsFeBr}}_{3}$.

Physical review. B, Condensed matterNov 1, 199269 citations

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

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}

{\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}

{\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.