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Physical review. B, Condensed matter

Elementary excitations in the spin-tube and spin-orbit models

Hanting Wang

Published Oct 3, 2001• 13 citations
Publisher

Abstract

A bond operator representation for three $S=\frac{1}{2}$ spins is obtained along the same line as the two-spin cases. With the spin and the chirality freedom expressed by the same bond operators, we studied the elementary excitations of the spin-tube and the spin-orbit models. For $3$-leg spin ladders and general spin ladders with an odd number of legs and periodic boundary conditions in the rung direction, the spinonlike excitations, which carry $\frac{1}{2}$ spin and chirality freedoms, are calculated by a variational ansatz. The magnonlike excitations, which denote the change of a dimerized bond from spin singlet to spin triplet and/or from chirality triplet to chirality singlet, or from one kind of chirality triplet to another chirality triplet, with different z-component, are also studied. Bound states of spinonlike excitation pairs exist near the vicinity of momentum zone center $\ensuremath{\pi}/2.$ The bond operators are also applied to other general spin-orbit models with spontaneously dimerized ground states, and the elementary excitations are studied.

DOI
10.1103/physrevb.64.174410

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We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i) for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii) for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii) between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.
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Characteristic properties of excited states in anitiferromagnetic ladder systems with spin-1/2 are investigated in relation with the theoretical analysis of the quite asymmetric shape of the peak for twice the spin gap Δg in magnetic Raman spectra. Here, the structure of exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which legs with antiferromagnetic bond Jc is connected by rungs with antiferromagnetic bond Jr. The singlet ground state in this system can be expressed as the ordering of singlet dimers on rungs in the ladder for Jc/Jr →+0. In fact, the value of 0.1 is adopted to be the ratio of Jc /Jr in order to discuss the experimental work of the magnetic Raman spectra for the ladder of V4+ ions in the oxide compound CaV2O5 reported in Konstantinović et al., Phys. Rev. B61 (2000), 15185. As for this peak of 2Δg , quite an asymmetric observed shape is explained by the present calculation. According to the analysis of spectra, we discuss the expression of excited states by triplet dimers on rungs: The dominant contribution of the pair of triplet dimers on adjacent rungs to the corresponding state for 2Δg peak is pointed out.