Spectral Properties of Quasi One-dimensional Quantum Antiferromagnets . Perturbative Continuous Unitary Transformations

In this work a perturbative realization of particle conserving continuous unitary transformations is applied to study the energies and the spectral properties of quasi one-dimensional quantum antiferromagnets. The systems considered are defined on a lattice and they allow for a perturbative decomposition. The unperturbed part is chosen to be a fully dimerized state. The groundstate is a product-state of singlets and the excitation spectrum is equidistant. The related energy quantum is called a triplon becaues it has total spin one. The continous unitary transformation leads to an effective triplon-conserving Hamiltonian and effective, experimentally relevant observables. The effective operators are obtained in a high-order series expansion in the perturbation parameters. All calculations are performed on finite clusters in real space and yield exact results in the thermodynamic limit due to the linked cluster theorem. The results are exact in the given order. In order to improve the representation of the results extrapolation techniques are used. A detailed description of extrapolation tools like standard Pade and dlogPade extrapolation, optimized perturbation theory and the use of internal parameters is given. The dimerized and frustrated spin-chain is analysed first. At zero frustration, a detailed investigation of the spectral weights shows that even in the limit of vanishing dimerization, the one-dimensional Heisenberg model, almost the total spectral weight is situated in the two-triplon sector. So, besides spinons, triplons may be used as elementary excitations for the one-dimensional Heisenberg model. The case of strong frustration is not yet settled. An extensive review of one- and two-triplon spectral densities at large and intermediate value of the dimerization for various values of the frustration is presented. The findings are compared with field theoretical results. In addition, the Raman response and the infrared absorption are investigated. Second, the antiferromagnetic two-leg Heisenberg ladder plus additional four-spin interaction is investigated. The transformation starts from the limit of isolated rung dimers. The excitations are rung-triplons. The relative energies of one-triplon states, the two-triplon bound states and the multi-triplon continua are given for various couplings. Optical observables are discussed in detail. The extent of the rung-singlet phase is calculated in the whole parameter space. It is shown that the experimental realizations of two-leg ladder systems are always situated in the rung-singlet phase. In the experimentally relevant regime, most of the spectral weight is captured by the one- and the two-triplon sector, but also three- and four-triplon contributions become sizable. The current understanding of the spectroscopic signatures of magnetic excitations in cuprate ladders measured with inelastic neutron scattering, Raman spectroscopy and infrared absorption is presented. The results obtained are compared with experimental findings. The first experimental evidence of a triplon-triplon bound state in a ladder system is found.