The quantum inverse transform method is applied to an anisotropic Heisenberg ferromagnet with a domain-wall-like ground state. The quantum Gelfand-Levitan-Marchenko equations are obtained and the profile of the domain wall is calculated.
We study a model for anisotropic ferromagnetic quantum domain walls. The large degeneracy of the ground state in the extreme anisotropic (Ising) limit, associated with the translational invariance of the ``kink center,'' is lifted in the quantum system in a peculiar way. The critical point, at which the Hamiltonian is invariant under the quantum group Uq [SU(2)], is exactly determined by a cluster method. We also find the ground state wave function at the critical point. Some generalizations of these results for arbitrary spin and dimension are obtained.
We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin 1∕2 chain. By numerical simulation, we find that the domain wall is dynamically stable in the Heisenberg-Ising model. Near the quantum critical point, the width of the domain wall diverges as ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.
We discuss entanglement in the spin-1∕2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a first-order quantum phase transition from a ferromagnetic to a kink-type phase, which is associated to a jump in the content of entanglement available in the system. Above the critical point, pairwise entanglement is shown to be nonvanishing and independent of the boundary magnetic field for large chains. Based on this result, we provide an analytical expression for the entanglement between arbitrary spins. Moreover, the effects of the quantum domains on the gapless region and for antiferromagnetic anisotropy are numerically analyzed. Finally multiparticle entanglement properties are considered, from which we establish a characterization of the critical anisotropy separating the gapless regime from the kink-type phase.
A variational calculation yields an eigenstate representing a domain wall-type solution for various quantum-mechanical spin models. Heisenberg Hamiltonians with local and exchange anisotropy, and an Ising model in a transverse field (including its critical regime) are discussed in detail. The domain walls are viewed as localized solutions of non-linear equations. The extent to which the results for the transverse field Ising model may be mapped on to a currently interesting “double well” anhurmonic lattice problem are analysed.
The propagation of a polarized ultrashort laser pulse is analyzed by the inverse scattering method under initial conditions including a spatial pulse profile, a state of the medium, and a “switched-on” resonant atom-field interaction. Magnetic degeneracy of atomic levels is taken into account. The Maxwell-Bloch equations are rewritten in Hamiltonian form without redefining the spatial and temporal variables. The inverse scattering method is based on an analysis of a new spectral problem. Gelfand-Levitan-Marchenko-type equations are derived, a soliton solution is obtained, and the changes in parameters of two solitons after their collision are calculated. A possible experimental setup for implementing the system under analysis is discussed.