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arXiv:cond-mat/0501295 · Physical Review Letters

Exact Analysis of ESR Shift in the Spin- 1/2 Heisenberg Antiferromagnetic Chain

Yoshitaka Maeda, Kazumitsu Sakai, Masaki Oshikawa

Published Jul 13, 2005• 28 citations
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Abstract

A systematic perturbation theory is developed for the ESR shift and is applied to the spin-1/2 Heisenberg antiferromagnetic chain with a general anisotropic exchange interaction. Using the Bethe ansatz technique, the resonance shift is obtained exactly for the whole range of temperature and magnetic field in the first order of the anisotropy. The obtained g shift strongly depends on magnetic fields at low temperature, showing a significant deviation from the previous classical result.

DOI
10.1103/physrevlett.95.037602

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A systematic perturbation theory is developed for the ESR shift and is applied to the spin-1/2 Heisenberg antiferromagnetic chain with a general anisotropic exchange interaction. Using the Bethe ansatz technique, the resonance shift is obtained exactly for the whole range of temperature and magnetic field in the first order of the anisotropy. The obtained g shift strongly depends on magnetic fields at low temperature, showing a significant deviation from the previous classical result.
A systematic field-theory approach to electron spin resonance (ESR) in the S=1/2S=1/2S=1/2 quantum antiferromagnetic chain at low temperature T (compared to the exchange coupling J) is developed. In particular, effects of a transverse staggered field h and an exchange anisotropy (including a dipolar interaction) \ensuremath{\delta} on the ESR line shape are discussed. In the lowest order perturbation theory, the linewidth is given as $\ensuremath{\propto}{\mathrm{Jh}}^{2}{/T}^{2}$ and $\ensuremath{\propto}(\ensuremath{\delta}{/J)}^{2}T,$ respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; nonperturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.
Electron spin resonance (ESR) is an important experimental technique. A comprehensive theory of ESR has been di cult to establish, and as such several di erent approximations are used to predict and explain experimental results. This thesis applies the bond-mean- eld theory to the problem of ESR frequency shift for the one-dimensional antiferromagnetic Heisenberg spin chain with uniaxial exchange anisotropy. We use this theory to calculate the ESR resonance frequency shift as a function of temperature and magnetic eld. We perform numerical calculations using the expression obtained. These results are compared to existing results in the literature; they are in broad agreement with theoretical results such as those of Oshikawa and A eck obtained via bosonisation, but they show discrepancies with experimental results. We agree with the theoretical authors that the discrepancy is due to our use of the simplest-case interaction model.
We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy, based on several effective field theories: the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free-fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid for thermodynamics, we have to take interactions among magnons into account in order to include the single-ion anisotropy as a perturbation. Although the O(3) NLSM is only valid in the Haldane phase, an appropriate translation of Faddeev-Zamolodchikov operators of the O(3) NLSM to fermion operators enables one to treat ESR shifts near the lower critical field in a similar manner to discussions in the Haldane phase. Our theory gives quantitative agreements with a numerical evaluation using quantum Monte Carlo simulation, and also with recent ESR experimental results on a spin-1 chain compound Ni(C5H14N2)2N3(PF6)\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{H}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}({\mathrm{PF}}_{6})Ni(C5​H14​N2​)2​N3​(PF6​).
We review our recent field-theory approach to ESR in quantum spin chains at low temperature. The perturbative expansion in an anisotropy is formulated systematically, avoiding previously made assumptions. The linewidth is calculated in the lowest order of the perturbation theory for a transverse staggered field and an exhange anisotropy. In the case of the transverse staggered field, the perturbative expansion become divergent at lower temperature. The spectrum in the zero energy limit is discussed using non-perturbative exact results on the sine-Gordon field theory. These theoretical results are compared to experimental data, particularly those on Cu benzoate.
A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy λλλ and magnetic field B. To demonstrate the accuracy, we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg model, and find that EPT successfully reproduces the exact Bethe Ansatz results for the ground state energy, the local magnetization, and the spin correlation functions (Bethe ansatz result is available for the first 7 lattice separations). In particular, EPT confirms for the first time the asymptotic behavior of the spin correlation functions predicted by the conformal field theory, which realizes only for lattice separations larger than 1000. Next, turning on the z-axis anisotropy and the magnetic field, the 2-spin and 4-spin correlation functions are calculated, and the results are compared with those obtained by Bosonization and density matrix renormalization group methods. Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state phase diagram in λλλ space is determined with help of the Roomany-Wyld RG finite-size-scaling. The results are in good agreement with those obtained by the level-spectroscopy method.