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arXiv:cond-mat/0505719 · Journal of the Physical Society of Japan

FractionalSzExcitation and Its Boundstate for theS=1/2 Antiferromagnetic Zigzag Spin Chain in a Magnetic Field

Kouichi Okunishi, Takashi Tonegawa

Published Jan 1, 2005• 4 citations
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Abstract

We demonstrate that domain-wall type excitations carrying the fractional magnetization $S^z=\pm1/3$ and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.

DOI
10.1143/jpsjs.74s.151

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We demonstrate that domain-wall type excitations carrying the fractional magnetization Sz=±1/3S^z=\pm1/3Sz=±1/3 and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.
We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag XXZ\mathrm{XXZ}XXZ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1/3$ and its bound state of ${S}^{z}=\ifmmode\pm\else\textpm\fi{}2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.
We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1\ensuremath{-}\frac{2}{N}$ (N=3,4,…)(N=3,4,\dots{})(N=3,4,…) plateau decays into NNN elementary excitations each carrying a fraction 1N\frac{1}{N}N1​ of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the M=0M=0M=0 plateau. Concentrating on the 13\frac{1}{3}31​ plateau (N=3)(N=3)(N=3) we unravel the microscopic structure of the domain walls which carry fractional spin-13\frac{1}{3}31​, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.
We study effects of a transverse magnetic field on the properties of the one-dimensional spin-1/2 Ising-like antiferromagnet. In order to emphasize the relevant role of domain walls between opposite antiferromagnetic domains, the spin Hamiltonian is exactly mapped to the interacting fermion Hamiltonian, via the dual transformation as well as the Jordan-Wigner transformation. Within the generalized Hartree-Fock approximation, we find that the excitation spectrum exhibits characteristic features, which are explained as a result of the different roles of the transverse field and of the transverse components of the exchange interactions in the propagation of the domain wall. At a critical field where the excitation gap vanishes, a ground-state phase transition is found to take place in the same manner as that in the transverse Ising model. In addition, we discuss the relevance of our magnetization curve with regard to experimental data in CsCoCl 3 .
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