We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phy
s. Rev. B 88, 155305 (2013) by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes.
We study kinks in the electronic dispersion of a generic strongly correlated system by dynamic mean-field theory (DMFT). The focus is on doped systems away from particle-hole symmetry where valence fluctuations matter potentially. Three different alg
orithms are compared to asses their strengths and weaknesses, as well as to clearly distinguish physical features from algorithmic artifacts. Our findings extend a view previously established for half-filled systems where kinks reflect the coupling of the fermionic quasiparticles to emergent collective modes, which are identified here as spin fluctuations. Kinks are observed when strong spin fluctuations are present and, additionally, a separation of energy scales for spin and charge excitations exists. Both criteria are met by strongly correlated systems close to a Mott-insulator transition. The energies of the kinks and their doping dependence fit well to the kinks in the cuprates, which is surprising in view of the spatial correlations neglected by DMFT.
