Solitary excitations in 1-d spin-chains

Details Solitary excitations in 1-d spin-chains Solitary excitations in 1-d spin-chains

2012-02-21

arxiv.org/abs/1202.4634v1

Physics

Condensed Matter

Strongly Correlated Electrons

6 pages including 5 figures and 2 tables

Scientific paper

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.

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