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arXiv · 1202.4634

Solitary excitations in one-dimensional spin chains

Anton Wöllert·Andreas Honecker
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Abstract

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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Anton Wöllert, Andreas Honecker. 2012-02-21. Solitary excitations in one-dimensional spin chains. https://doi.org/10.1103/physrevb.85.184433

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