Dynamics of spin ladders

We derive an approximate theory for Heisenberg spin ladders with two legs by mapping the spin dynamics onto the problem of hard-core "bond bosons." The parameters of the bosonic Hamiltonian are obtained by matching anomalous Green's functions to Lanczos results and we find evidence for a strong renormalization due to quantum fluctuations. Various dynamical spin correlation functions are calculated and found to be in good agreement with Lanczos results. We then enlarge the effective Hamiltonian to describe the coupling of the bosonic spin fluctuations to a single hole injected into the system and treat the hole dynamics within the rainbow-diagram approximation of Schmitt-Rink et nl. Theoretical predictions for the single-hole spectral function are obtained and found to be in good agreement with Lanczos results.