69 research outputs found
Interfaces and droplets in quantum lattice models
This paper is a short review of recent results on interface states in the
Falicov-Kimball model and the ferromagnetic XXZ Heisenberg model. More
specifically, we discuss the following topics: 1) The existence of interfaces
in quantum lattice models that can be considered as perturbations of classical
models. 2) The rigidity of the 111 interface in the three-dimensional
Falicov-Kimball model at sufficiently low temperatures. 3) The low-lying
excitations and the scaling of the gap in the 111 interface ground state in the
ferromagnetic XXZ Heisenberg model in three dimensions. 4) The existence of
droplet states in the XXZ chain and their properties.Comment: 7 pages, 1 figure (embedded eps). For the proceedings of the XIII
International Congress of Mathematical Physics, London, July 18-24, 200
A continuum approximation for the excitations of the (1,1,...,1) interface in the quantum Heisenberg model
It is shown that, with an appropriate scaling, the energy of low-lying
excitations of the (1,1,...,1) interface in the -dimensional quantum
Heisenberg model are given by the spectrum of the -dimensional Laplacian
on an suitable domain.Comment: Latex, 12 page
Curvature stabilized skyrmions with angular momentum
We examine skyrmionic field configurations on a spherical ferromagnet with
large normal anisotropy. Exploiting variational concepts of angular momentum we
find a new family of localized solutions to the Landau-Lifshitz equation that
are topologically distinct from the ground state and not equivariant.
Significantly, we observe an emergent spin-orbit coupling on the level of
magnetization dynamics in a simple system without individual rotational
invariance in spin and coordinate space
A generalised Landau-Lifshitz equation for isotropic SU(3) magnet
In the paper we obtain equations for large-scale fluctuations of the mean
field (the field of magnetization and quadrupole moments) in a magnetic system
realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We
use the generalized Heisenberg Hamiltonian with biquadratic exchange as a
quantum model. A quantum thermodynamical averaging gives classical effective
models, which are interpreted as Hamiltonian systems on coadjoint orbits of Lie
group SU(3).Comment: 15 pages, 1 figur
Two-Dimensional Toda-Heisenberg Lattice
We consider a nonlinear model that is a combination of the anisotropic
two-dimensional classical Heisenberg and Toda-like lattices. In the framework
of the Hirota direct approach, we present the field equations of this model as
a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy,
and derive its N-soliton solutions
Isolated Eigenvalues of the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions
We investigate the low-lying excited states of the spin J ferromagnetic XXZ
chain with Ising anisotropy Delta and kink boundary conditions. Since the third
component of the total magnetization, M, is conserved, it is meaningful to
study the spectrum for each fixed value of M. We prove that for J>= 3/2 the
lowest excited eigenvalues are separated by a gap from the rest of the
spectrum, uniformly in the length of the chain. In the thermodynamic limit,
this means that there are a positive number of excitations above the ground
state and below the essential spectrum
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