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arXiv:cond-mat/0307121 · Physical review. B, Condensed matter

Fractional Sz excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

Kouichi Okunishi, Takashi Tonegawa

Published Dec 23, 2003• 44 citations
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Abstract

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag $\mathrm{XXZ}$ 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.

DOI
10.1103/physrevb.68.224422

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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.
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We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.
Spin fractionalization and zero modes in the spin-12\frac{1}{2}21​ XXZ chain with boundary fields
In this work we argue that the antiferromagnetic spin 12\frac{1}{2}21​ XXZ chain in the gapped phase with boundary magnetic fields hosts fractional spin 14\frac{1}{4}41​ at its edges. Using a combination of Bethe ansatz and the density matrix renormalization group we show that these fractional spins are sharp quantum observables in both the ground and the first excited state as the associated fractional spin operators have zero variance. In the limit of zero edge fields, we argue that these fractional spin operators once projected onto the low energy subspace spanned by the ground state and the first excited state, identify with the strong zero energy mode discovered by P. Fendley \cite{Fendley}.
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