Abstract
We study two dimensional soliton solutions in the $CP^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction. First, we derive such a model as a continuous limit of the $SU(3)$ tilted ferromagnetic Heisenberg model on a square lattice. Then, introducing an additional potential term to the derived Hamiltonian, we obtain exact soliton solutions for particular sets of parameters of the model. The vacuum of the exact solution can be interpreted as a spin nematic state. For a wider range of coupling constants, we construct numerical solutions, which possess the same type of asymptotic decay as the exact analytical solution, both decaying into a spin nematic state.
Highlights
In the 1960s, Skyrme introduced a (3 þ 1)-dimensional Oð4Þ nonlinear (NL) sigma model [1,2], which is well known as a prototype of a classical field theory that supports topological solitons (See Ref. [3], for example)
For a wider range of coupling constants, we construct numerical solutions, which possess the same type of asymptotic decay as the exact analytical solution, both decaying into a spin nematic state
Since we are interested in constructing topological solitons, we consider the case when the physical space R2 can be compactified to the sphere S2, i.e., the field Z takes some fixed value on the spatial boundary
Summary
In the 1960s, Skyrme introduced a (3 þ 1)-dimensional Oð4Þ nonlinear (NL) sigma model [1,2], which is well known as a prototype of a classical field theory that supports topological solitons (See Ref. [3], for example). The SUð3Þ FM Heisenberg model may play an important role in diverse physical systems ranging from string theory [33] to condensed matter, or quantum optical three-level systems [34] It can be derived from a spin-1 bilinearbiquadratic model with a specific choice of coupling constants, so-called FM SUð3Þ point; see, e.g., Ref. We study baby skyrmion solutions of an extended CP2 NLσ model composed of the CP2 Dirichlet term, a DM type interaction term, i.e., the Lifshitz invariant, and a potential term.
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