Abstract
We present a study of the dynamic structure factor of the antiferromagnetic spin-$\frac{1}{2}$ 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 factors 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.
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