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We investigate weakly coupled spin-1/2 ladders in a magnetic field. The workis motivated by recent experiments on the compound$\mathrm{(C_5H_{12}N)_2CuBr_4}$ (BPCB). We use a combination of numerical andanalytical methods, in particular the density matrix renormalization group(DMRG) technique, to explore the phase diagram and the excitation spectra ofsuch a system. We give detailed results on the temperature dependence of themagnetization and the specific heat, and the magnetic field dependence of thenuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupledladders, treating the weak interladder coupling within a mean field approach,we compute the transition temperature of triplet condensation and itscorresponding antiferromagnetic order parameter. Existing experimentalmeasurements are discussed and compared to our theoretical results. Furthermorewe compute, using time dependent DMRG, the dynamical correlations of a singlespin ladder. Our results allow to directly describe the inelastic neutronscattering cross section up to high energies. We focus on the evolution of thespectra with the magnetic field and compare their behavior for differentcouplings. The characteristic features of the spectra are interpreted usingdifferent analytical approaches such as the mapping onto a spin chain, aLuttinger liquid (LL) or onto a t-J model. For values of parameters for whichsuch measurements exist, we compare our results to inelastic neutron scatteringexperiments on the compound BPCB and find excellent agreement. We makeadditional predictions for the high energy part of the spectrum that arepotentially testable in future experiments.

Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field (PhD thesis)