Solitary excitations in one-dimensional spin chains

We study the real-time evolution of solitary excitations in one-dimensional quantum spin chains using exact diagonalization and the density-matrix renormalization group. The underlying question of this work is the correspondence between classical solitons and solitons in quantum mechanics. While classical solitons as eigensolutions of nonlinear wave equations are localized and have a sharp momentum, this is not possible in the corresponding quantum case due to the linearity of the Schrodinger equation or, seen in a more pictorial way, because of the uncertainty relation. For the case of the XXZ model it is shown that the real-time evolution of quantum wave packets accompanied by spreading is in qualitative accordance with that predicted by classical solitons.