2005
DOI: 10.1103/physrevb.72.104438
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N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

Abstract: We investigate the low-energy properties, especially the low-energy excitation structures, 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, together with a saddle-point approximation. This strategy is valid in the weak interchain (rung) coupling regime. We show… Show more

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Cited by 18 publications
(7 citation statements)
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References 89 publications
(200 reference statements)
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“…For an odd number of legs, the lowest magnon band of the model (2) is six-fold degenerate, compared to the three-fold degeneracy of non-frustrated systems, namely tubes with an even number of legs or ladders. [30][31][32] Turning on a uniform or nonuniform magnetic field, Sato predicted a succession of quantum phase transitions between critical phases as the field is increased, along with again an even-odd effect. 30 Introducing an asymmetry in the rung couplings, a NLSM analysis and DMRG results have shown the existence of 2S quantum phase transitions between gapped phases when varying the anisotropy parameter.…”
Section: A the Modelmentioning
confidence: 99%
“…For an odd number of legs, the lowest magnon band of the model (2) is six-fold degenerate, compared to the three-fold degeneracy of non-frustrated systems, namely tubes with an even number of legs or ladders. [30][31][32] Turning on a uniform or nonuniform magnetic field, Sato predicted a succession of quantum phase transitions between critical phases as the field is increased, along with again an even-odd effect. 30 Introducing an asymmetry in the rung couplings, a NLSM analysis and DMRG results have shown the existence of 2S quantum phase transitions between gapped phases when varying the anisotropy parameter.…”
Section: A the Modelmentioning
confidence: 99%
“…[4] and [27]) very few works consider ladders with S > 1/2. In particular, the N -leg spin-1 Heisenberg ladder was studied by the use of bozonization [28,29], Monte Carlo [30], and perturbation theory methods [31] and by using the nonlinear σ model approach [20,21,32] (see also Ref. [12]).…”
Section: Introductionmentioning
confidence: 99%
“…Introduction.-Spin tubes constitute a special class of quasi-one-dimensional spin ladder systems characterized by periodic boundary conditions in the rung direction [1][2][3][4][5][6][7][8][9][10][11][12][13]. The magnetic compound ½ðCuCl 2 tachHÞ 3 ClCl 2 , for sample preparation, see [14], is a geometrically frustrated triangular spin tube, the frustration being related both to the triangular arrangement of its rungs and to the twisted geometry of the legs, compare Fig.…”
mentioning
confidence: 99%
“…1(a). The relatively simple exchange pathway structure, that thanks to high symmetry is described by only two dominant Heisenberg exchange couplings [15], as well as the extremely weak exchange interactions between neighboring tubes, renders ½ðCuCl 2 tachHÞ 3 ClCl 2 an excellent real material to study general properties of the spin-tube systems [4,6,9,11]. An appropriate spin Hamiltonian describing the magnetic properties of this material reads as…”
mentioning
confidence: 99%