Solitary excitations in one-dimensional spin chains

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 Schrödinger 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.

6 pages including 5 figures and 2 tables

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• Bose condensation in flat bands
• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Quantum Dynamics of Solitons in Strongly Interacting Systems on Optical Lattices

Cited by in corpus (8)

• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Quasi-soliton scattering in quantum spin chains
• Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies
• Getting through to a qubit by magnetic solitons
• Propagation and jamming dynamics in Heisenberg spin ladders
• Single-qubit remote manipulation by magnetic solitons
• Slow transport and bound states for spinless fermions with long-range Coulomb interactions on one-dimensional lattices
• Generation of chiral solitons in antiferromagnetic chains by a quantum quench