Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1201.5170 · Physical Review B

Field theory analysis of S=1 antiferromagnetic bond-alternating chains in the dimer phase

Junya Tamaki, Masaki Oshikawa

Published Apr 19, 2012• 3 citations
arXivHTMLPDF

Abstract

Dynamics of $S=1$ antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C${}_{9}$H${}_{24}$N${}_{4}$)(NO${}_{2}$)ClO${}_{4}$ (abbreviated as NTENP). We derive a sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks corresponding to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.

DOI
10.1103/physrevb.85.134431

Related papers

Spin excitations under fields in an anisotropic bond-alternating quantum S=1 chain: contrast with Haldane spin chains

Masayuki Hagiwara, L. P. Régnault, A. Zheludev +8 more

Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].

arXiv:cond-mat/0501207•Jan 10, 2005•0 citations

Dynamical properties of S=1 bond-alternating Heisenberg chains in transverse magnetic fields

Takahumi Suzuki, Sei-ichiro Suga

We calculate dynamical structure factors of the $S=1$ bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed in the viewpoint of the field dependence of the excitation continuum. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the $S=1$ bond-alternating Heisenberg-chain compound $\mathrm{Ni}({\mathrm{C}}_{9}{\mathrm{D}}_{24}{\mathrm{N}}_{4})(\mathrm{N}{\mathrm{O}}_{2})\mathrm{Cl}{\mathrm{O}}_{4}$ and the $S=1$ Haldane-gap compound $\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{D}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}(\mathrm{P}{\mathrm{F}}_{6})$ in transverse magnetic fields.

arXiv:cond-mat/0505196•Physical Review B•Jul 15, 2005•8 citations

Distribution of exchange energy in a bond-alternating S=1 quantum spin chain

A. Zheludev, Takatsugu Masuda, B. C. Sales +4 more

The quasi-one-dimensional bond-alternating $S=1$ quantum antiferromagnet [Ni${(N,N}^{\ensuremath{'}}$$\ensuremath{-}\mathrm{b}\mathrm{i}\mathrm{s}(3\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l})\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{e}\ensuremath{-}1,3\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}(\ensuremath{\mu}\ensuremath{-}{\mathrm{NO}}_{2})]{\mathrm{ClO}}_{4}$ (NTENP) is studied by single-crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron-scattering intensities are also analyzed, using the first-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground-state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principles density-matrix renormalization-group calculations are used to study the relation between these two quantities.

arXiv:cond-mat/0310741•Physical Review B•Apr 16, 2004•21 citations

Spin Excitations in an Anisotropic Bond-Alternating Quantum S=1 Chain in a Magnetic Field: Contrast to Haldane Spin Chains

Masayuki Hagiwara, L. P. Régnault, A. Zheludev +8 more

Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].

Physical Review Letters•May 4, 2005•45 citations

Dynamical structure factors of S=1 bond-alternating Heisenberg chains

Takahumi Suzuki, Sei-ichiro Suga

We calculate the dynamical structural factor of the $S=1$ bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~{q}_{c}$ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in $0<~q<~{q}_{c}.$ As the bond-alternation becomes strong, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is $93%,$ which is slightly smaller than that in the $S=1$ Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.

arXiv:cond-mat/0309178•Physical review. B, Condensed matter•Oct 17, 2003•5 citations

Tomonaga-Luttinger Liquid in a Quasi-One-Dimensional S=1 Antiferromagnet Observed by Specific Heat Measurements

Masayuki Hagiwara, H. Tsujii, Costel R. Rotundu +6 more

Specific-heat experiments on single crystals of the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9H24N4)(NO2)ClO2 (NTENP) have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C(mag)) is proportional to temperature (T) above a critical field H(c), at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C(mag)/T increases as the magnetic field approaches H(c) from above. The data are in good quantitative agreement with the prediction of the c= 1 conformal field theory in conjunction with the velocity of the excitations calculated by a numerical diagonalization, providing conclusive evidence for a Tomonaga-Luttinger liquid.

arXiv:cond-mat/0511004•Physical Review Letters•Apr 12, 2006•28 citations
Dynamics of S=1S=1S=1 antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C9{}_{9}9​H24{}_{24}24​N4{}_{4}4​)(NO2{}_{2}2​)ClO4{}_{4}4​ (abbreviated as NTENP). We derive a sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks corresponding to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].
We calculate dynamical structure factors of the S=1S=1S=1 bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed in the viewpoint of the field dependence of the excitation continuum. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the S=1S=1S=1 bond-alternating Heisenberg-chain compound Ni(C9D24N4)(NO2)ClO4\mathrm{Ni}({\mathrm{C}}_{9}{\mathrm{D}}_{24}{\mathrm{N}}_{4})(\mathrm{N}{\mathrm{O}}_{2})\mathrm{Cl}{\mathrm{O}}_{4}Ni(C9​D24​N4​)(NO2​)ClO4​ and the S=1S=1S=1 Haldane-gap compound Ni(C5D14N2)2N3(PF6)\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{D}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}(\mathrm{P}{\mathrm{F}}_{6})Ni(C5​D14​N2​)2​N3​(PF6​) in transverse magnetic fields.
The quasi-one-dimensional bond-alternating S=1S=1S=1 quantum antiferromagnet [Ni${(N,N}^{\ensuremath{'}}$$\ensuremath{-}\mathrm{b}\mathrm{i}\mathrm{s}(3\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l})\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{e}\ensuremath{-}1,3\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}(\ensuremath{\mu}\ensuremath{-}{\mathrm{NO}}_{2})]{\mathrm{ClO}}_{4}$ (NTENP) is studied by single-crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron-scattering intensities are also analyzed, using the first-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground-state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principles density-matrix renormalization-group calculations are used to study the relation between these two quantities.
Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].
We calculate the dynamical structural factor of the S=1S=1S=1 bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in 0< q< qc0<~q<~{q}_{c}0< q< qc​ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in 0< q< qc.0<~q<~{q}_{c}.0< q< qc​. As the bond-alternation becomes strong, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is 9393%,93 which is slightly smaller than that in the S=1S=1S=1 Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.
Specific-heat experiments on single crystals of the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9H24N4)(NO2)ClO2 (NTENP) have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C(mag)) is proportional to temperature (T) above a critical field H(c), at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C(mag)/T increases as the magnetic field approaches H(c) from above. The data are in good quantitative agreement with the prediction of the c= 1 conformal field theory in conjunction with the velocity of the excitations calculated by a numerical diagonalization, providing conclusive evidence for a Tomonaga-Luttinger liquid.