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arXiv:cond-mat/0201098 · Journal of Physics Condensed Matter

Spin dynamics of theS= 1/2 antiferromagnetic zig-zag ladder with anisotropy

Pedro D Sacramento, Vitor Rocha Vieira

Published Dec 24, 2001• 3 citations
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Abstract

We use exact diagonalization and the modified Lanczos method to study the finite-energy and finite-momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In the gapless regime we find a sharp low-energy peak in the structure function for the transverse spin excitations, consistent with a finite stiffness.

DOI
10.1088/0953-8984/14/3/326

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We use exact diagonalization and the modified Lanczos method to study the finite-energy and finite-momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In the gapless regime we find a sharp low-energy peak in the structure function for the transverse spin excitations, consistent with a finite stiffness.
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Abstract. We study the ground state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field vs interchain coupling strength. The first one corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second one represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase. PACS numbers: 75.10.Jm Quantized spin models, 75.10.Pq Spin chain modelsSpin Ladder with Anisotropic Ferromagnetic Legs in a Transverse Magnetic Field 2 1.
We study the opening of the Haldane gap in two-leg and four-leg anisotropic spin ladders using bosonization and renormalization group methods, and we determine the phase diagram as a function of the interchain coupling and relative anisotropy Jz/Jxy.{J}^{z}{/J}^{\mathrm{xy}}.Jz/Jxy. It is found that the opening of the Haldane gap is qualitatively different for the two cases considered. For the two-leg ladder the Haldane gap opens for arbitrarily small interchain coupling, independent of Jz/Jxy,{J}^{z}{/J}^{\mathrm{xy}},Jz/Jxy, and the Haldane phase exists in a large region of parameter space. For the four-leg ladder the opening of the Haldane gap is strongly dependent on both the interchain coupling as well as Jz/Jxy,{J}^{z}{/J}^{\mathrm{xy}},Jz/Jxy, and the Haldane phase exists only in a narrow region about the isotropic antiferromagnet.
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