The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two-dimensional lattice and their stability

In this paper, we present a scheme for the construction of quantum states of vortex-like topological excitations corresponding to spin-1/2 strongly XY-anisotropic nearest neighbor Heisenberg ferromagnet on two-dimensional lattice. The procedure involving Pauli spin basis states is carried out corresponding to both infinite dilute limit and finite density limit of vortex/anti-vortex. It is found that the corresponding quantum mechanical states representing charge 1 quantum vortices/anti-vortices can be expressed as linear combinations of single magnon states, composite multi-magnon states and the ground state. Detailed calculations show that these states are quantum mechanically stable states of the Hamiltonian only when the system size exceeds certain threshold value. Our analysis indicates that the interactions between different magnon modes can very well generate these topological excitations. Possible applications of our calculations to real magnetic systems are also discussed. Magnetic measurements probing spin dynamics may be undertaken to verify the existence of the threshold size for the stability of vortices.