1202.4634 (Anton Wöllert et al.)

Solitary excitations in 1-d spin-chains    [PDF]

Anton Wöllert, Andreas Honecker

We study the real-time evolution of solitary excitations in 1-d quantum spin
chains using exact diagonalization (ED) and the density-matrix renormalization
group (DMRG). The underlying question of this work is the correspondence
between classical solitons and solitons in quantum mechanics. While classical
solitons as eigensolutions of non-linear wave equations are localized and have
a sharp momentum, this is not possible in the corresponding quantum case due to
the linearity of the Schr\"odinger 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 the one predicted by classical solitons.

View original: http://arxiv.org/abs/1202.4634