Solitary excitations in one-dimensional spin chains

TL;DR

This paper investigates the real-time behavior of solitary excitations in one-dimensional quantum spin chains, comparing quantum wave packet evolution with classical soliton predictions using ED and DMRG methods.

Contribution

It demonstrates the qualitative agreement between quantum wave packet dynamics and classical soliton behavior in the XXZ model.

Findings

Quantum wave packets spread over time, resembling classical soliton evolution.

Classical solitons' localized nature is not fully preserved in quantum dynamics.

Quantum and classical soliton behaviors show qualitative correspondence.

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.