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arXiv:1109.0063 · Physical Review B

Spin-chirality separation and S3 symmetry breaking in the magnetization plateau of the quantum spin tube

Kouichi Okunishi, Masahiro Sato, Tôru Sakai, Kiyomi Okamoto, Chigak Itoi

Published Feb 14, 2012• 18 citations
arXivHTMLPDF

Abstract

We study the magnetization plateau state of the three-leg spin-$\frac{1}{2}$ tube in the strong rung coupling region, where ${S}_{3}$ symmetry breaking and the low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless nonmagnetic excitations, the spin-imbalance phase, and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.

DOI
10.1103/physrevb.85.054416

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We study the magnetization plateau state of the three-leg spin-12\frac{1}{2}21​ tube in the strong rung coupling region, where S3{S}_{3}S3​ symmetry breaking and the low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless nonmagnetic excitations, the spin-imbalance phase, and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.
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In this paper, we investigate the properties of frustrated three-leg spin-SSS tubes under a magnetic field. We concentrate on two kind of geometries for these tubes, one of which is relevant for the compound [(CuCl2tachH)3Cl]Cl2[{({\mathrm{CuCl}}_{2}\mathrm{tachH})}_{3}\mathrm{Cl}]{\mathrm{Cl}}_{2}[(CuCl2​tachH)3​Cl]Cl2​. We perform an analytical large-SSS path-integral approach to determine the phase diagrams, which exhibit several magnetization plateaux. Moreover, by combining the field-theory approach with a strong-coupling one, we also investigate the issue of gapless nonmagnetic excitations on some plateaux, dubbed chirality degrees of freedom for both tubes: on increasing the intertriangle exchange couplings, a gapless chiral phase transforms into a gapped ``ferrochiral'' state, possibly through intermediate ``spin-imbalanced'' states. All these predictions are confirmed numerically using large-scale density-matrix renormalization-group simulations for the S=3/2S=3/2S=3/2 case.
Using the density-matrix renormalization group and exact diagonalization methods the ground-state properties of the S = 3/2 three-leg Heisenberg tube with leg ( J ||) and rung ( J ⊥) exchange couplings are studied. We find that the spin-excitation gap associated with a spontaneous dimerization opens in the entire region of the coupling strength, as seen in the S = 1/2 three-leg tube. However, in contrast to the case of the S = 1/2 tube, the gap develops very slowly with increasing the rung coupling strength in the weak-coupling regime and its size remains only about 5 % of the leg coupling strength even at J ⊥/ J || = 5. We also calculate the quantized Berry phase and suggest that there exist three types of the valence-bond-solid states depending on the ratio of leg and rung coupling strengths. Moreover, an effective model is derived by the perturbative expansion to check the numerical results in the strong rung-coupling limit.
Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the S = 1/2 three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in the case of the regular-triangle unit cell when the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to a gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: Néel, dimer, chiral and/or inhomogeneous orders, a new mechanism for the magnetization plateau formation, and others. The recently synthesized spin tube materials are also briefly introduced.