N-leg integer-spin ladders and tubes in commensurate external fields -Nonlinear sigma model approach-

Abstract

We investigate the low-energy properties of N-leg integer-spin ladders and tubes with an antiferromagnetic (AF) intrachain coupling. In the odd-leg tubes, the AF rung coupling causes the frustration. To treat all ladders and tubes systematically, we apply Sénéchal's method [Phys. Rev. B 52, 15319 (1995)], based on the nonlinear sigma model. This strategy is valid in the weak interchain (rung) coupling regime. We show that all frustrated tubes possess six-fold degenerate spin-1 magnon bands, as the lowest excitations, while other ladders and tubes have a standard triply degenerate bands. We also consider effects of four kinds of Zeeman terms: uniform, staggered only along the rung, only along the chain, or both directions. The above prediction of the no-field case implies that a sufficiently strong uniform field yields a two-component Tomonaga-Luttinger liquid (TLL) due to the condensation of doubly degenerate lowest magnons in frustrated tubes. In contrast, the field induces a standard one-component TLL in all other systems. This is supported by symmetry and bosonization arguments based on the Ginzburg-Landau theory. The bosonization also suggests that the two-component TLL vanishes and a one-component TLL appears, when the uniform field becomes larger for the second lowest magnon bands to touch the zero-energy line. This transition could be observed as a cusp singularity in the magnetization process. All the analyses for the systems with a staggered Zeeman term suggest that the emergence of the doubly degenerate transverse magnons and the single longitudinal one is universal for the one-dimensional AF spin systems with weak staggered field.

26 pages, 18 figures, Revtex. published version. see also short articles, cond-mat/0410419 and cond-mat/0511024

References in corpus (5)

• Magnetic phase diagram of the S=1/2 antiferromagnetic zigzag spin chain in the strongly frustrated region: cusp and plateau
• Magnetic characterization of the frustrated three-leg ladder compound [(CuCl2tachH)3Cl]Cl2
• Soliton binding and low-lying singlets in frustrated odd-legged S=1/2 spin tubes
• Coupled $S=1/2$ Heisenberg antiferromagnetic chains in an effective staggered field
• Low-energy properties of two-leg spin-1 antiferromagnetic ladders with commensurate external fields and their extensions

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• Combined analytical and numerical approach to magnetization plateaux in one-dimensional spin tube antiferromagnets
• Magnon bands of N-leg integer-spin antiferromagnetic systems in the weak interchain-coupling regime
• Topological phases in two-legged Heisenberg ladders with alternating interactions
• Low-energy effective theory and two distinct critical phases in a spin-1/2 frustrated three-leg spin tube
• Frustration-induced exotic properties of magnetic molecules
• Quantum order by disorder in Frustrated Spin Nanotubes
• Nonlinear sigma model of a spin ladder containing a static single hole