Elementary excitations in quantum magnets can be typically described in terms of long-lived quasiparticles, either simple magnons (spin waves), or more exotic fractionalized excitations such as spinons. In general, when multiple quasiparticles are present, they interact, and in a strongly correlated system, they interact strongly. We employ MPS-based techniques to uncover signatures of interactions between quasiparticles that show up in the dynamical spin correlations of antiferromagnets in presence of a magnetic field.
In this talk, I will first focus on the antiferromagnetic spin-1/2 chain, addressing both the low and high magnetization regimes. In the low magnetization regime, in the gapless phase, we find that the marginally irrelevant backscattering interaction between the fractionalized spinons leaves a distinct signature in the transverse dynamical susceptibility creating a non-zero gap between two branches of excitations at small momentum. In the high magnetization regime, close to the saturation field, we show that interactions between magnons lead to a formation of two-magnon bound states which leave a sharp feature in the transverse correlations. I will then address two-dimensional antiferromagnets, where our studies of the dynamical correlations on finite-circumference cylinders suggest that the presence of two-magnon bound states in the high magnetization regime is not unique to 1D.