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arXiv:cond-mat/0204489 · Physical review. B, Condensed matter

Field-induced gap in the spin- 12 antiferromagnetic Heisenberg chain: A density-matrix renormalization-group study

Jizhong Lou, Shaojin Qin, Changfeng Chen, Zhao-Bin Su, Lu Yu

Published Jan 17, 2002• 21 citations
arXivHTMLPDF

Abstract

We study the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetization, and spin correlation functions are found. Careful examination of the low energy properties and magnetization reveals interesting competing effects of the staggered and uniform fields. The incommensurate behavior in the spin correlation functions is demonstrated and discussed in detail. The present work reproduces earlier results in good agreement with experimental data on copper benzoate and predicts new interesting field-induced features at very high magnetic field.

DOI
10.1103/physrevb.65.064420

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We study the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetization, and spin correlation functions are found. Careful examination of the low energy properties and magnetization reveals interesting competing effects of the staggered and uniform fields. The incommensurate behavior in the spin correlation functions is demonstrated and discussed in detail. The present work reproduces earlier results in good agreement with experimental data on copper benzoate and predicts new interesting field-induced features at very high magnetic field.
We consider the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain in a staggered magnetic field describing materials such as copper benzoate and copper pyrimidine dinitrate. Using the density matrix renormalization group for transfer matrices (TMRG) we calculate the magnetization of these materials at finite temperature and arbitrary magnetic field. These results are in excellent agreement with experimental data, allowing for a determination of the inhomogeneity parameter ccc of copper benzoate (c=0.043)(c=0.043)(c=0.043) and copper pyrimidine dinitrate (c=0.11)(c=0.11)(c=0.11). The TMRG approach can be applied to rather low temperatures, yielding singular field and temperature dependences of susceptibilities.
A recent study [J. Lou, et al., Phys. Rev. Lett. 94, 217207 (2005)] reveals that topological edge effects induce bound midgap states in antiferromagnetic Heisenberg chains with a staggered magnetic field. We report density matrix renormalization group calculations that examine the effects of high magnetic field on the gap and midgap states and the range of validity of the field theory prediction on their scaling behavior. We also investigate the effects of the site parity (i.e., even or odd number of sites in the chain), the dilution of the spin chain by dopant atoms, and the uniform magnetic field on the emergence and evolution of the midgap states. The results provide useful insights into the behavior of the edge excitations in spin chain materials, which should facilitate the comparison between theory and experiment and stimulate further investigations.
Using the density-matrix-renormalization-group technique, we calculate numerically the low-energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of the ${R}_{2}{\mathrm{BaNiO}}_{5} (R\ensuremath{\ne}Y)$ family below the N\'eel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the nonlinear $\ensuremath{\sigma}$ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization.
We measured the magnetization processes of the S = 1/2 antiferromagnetic chain compound, Cu benzoate. From the inelastic neutron scattering and the specific heat measurements it was recently discovered that the substance exhibits an unexpected gap which varies approximately as the 2/3 power of an applied magnetic field. The primary mechanism of the gap formation is produced by an effective staggered field due to both the alternating g-tensor and the Dzyaloshinskii-Moriya interaction. We observed the effect of the effective staggered field on the magnetization process of Cu benzoate as a rounding behavior near the saturation field as well as an initial nonlinear increment near zero field. The experimental results are well reproduced by the numerical calculation on the Hamiltonian which includes the appropriate term of the staggered field, using the finite temperature density matrix renormalization group method.
Recent experiments on the S=12S=\frac{1}{2}S=21​ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the 23\frac{2}{3}32​ power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the S=12S=\frac{1}{2}S=21​ chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function, and field and temperature dependence of the total susceptibility.
Magnetic excitations in copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating ggg-tensor and Dzyaloshinskii-Moriya interactions that exhibits a field-induced spin gap, are probed by means of pulsed-field electron-spin-resonance spectroscopy. In particular, we report on a minimum of the gap in the vicinity of the saturation field Hsat=48.5{H}_{\mathrm{sat}}=48.5Hsat​=48.5 T associated with a transition from the sine-Gordon region (with soliton-breather elementary excitations) to a spin-polarized state (with magnon excitations). This interpretation is fully confirmed by the quantitative agreement over the entire field range of the experimental data with the density matrix renormalization group calculations for a spin-1/2 Heisenberg chain with a staggered transverse field.