Spin-Dynamics of the antiferromagnetic S=1/2-Chain at finite magnetic Fields and intermediate Temperatures

We present a study of the dynamic structure factor of the antiferromagnetic spin-1/2 Heisenberg chain at finite temperatures and finite magnetic fields. Using Quantum-Monte-Carlo based on the stochastic series expansion and Maximum-Entropy methods we evaluate the longitudinal and the transverse dynamic structure factor from vanishing magnetic fields up to and above the threshold $B_c$ for ferromagnetic saturation, as well as for high and for intermediate temperatures. We study the field-induced redistribution of spectral weight contrasting longitudinal versus transverse excitations. At finite fields below saturation incommensurate low-energy modes are found consistent with zero temperature Bethe-Ansatz. The crossover between the field induced ferromagnet above $B_c$ and the Luttinger liquid below $B_c$ is analyzed in terms of the transverse spin-dynamics. Evaluating sum-rules we assess the quality of the analytic continuation and demonstrate excellent consistency of the Maximum-Entropy results.