Spin Excitations in Low-Dimensional Quantum Antiferromagnets

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In this thesis we have investigated and compared the spin excitations of several low-dimensional quantum antiferromagnets, including the one-dimensional spin-1/2 chain, the one-dimensional
spin-1 chain, the two-leg spin-1/2 ladder, the four-leg spin-1/2 ladder, the two-dimensional spin-1/2 antiferromagnet, a bilayer containing two coupled spin-1/2 planes and the two-dimensional spin-1 antiferromagnet. Besides a nearest-neighbor Heisenberg interaction the in uence of a cyclic four-spin exchange on the properties of a two-leg ladder has been considered. Furthermore, the effect of spin phonon interaction on the magnetic excitations of the two-dimensional antiferromagnets has been analyzed. For these investigations several analytical and numerical techniques have been employed. The two-dimensional antiferromagnets have been treated within interacting spin-wave theory. For the investigation of the spin-1/2 chain and the two-leg spin-1/2 ladder a fermionic representation, which is based on the Jordan-Wigner transformation, has been applied. The Density Matrix Renormalization Group (DMRG) has been used to analyze the properties of the one-dimensional spin-1 chain, the two-leg spin-1/2 ladder and the four-leg spin-1/2 ladder.