Abstract
In this talk I shall try to convey to you that the interaction betweencollective excitations originating from a strongly anisotropic quantumHeisenberg ferromagnet on two dimensional lattices, can very well lead tothe formation of localized topological excitations of vortex/anti-vortextype. This happens below the Berezinskii-Kosterlitz-Thouless transitiontemperature (𝑇𝐵𝐾𝑇) when vortices andanti-vortices are immobile and remain as bound pairs. I will describe ourconstruction of quantum states of vortex like topological excitationscorresponding to spin-1/2 strongly XY- anisotropic nearest neighbourHeisenberg ferromagnet on two-dimensional lattice. The procedure involvesthe Pauli spin basis states and is carried out corresponding to bothinfinite dilute limit and finite density limit of vortex/anti-vortex. Itis found that the corresponding quantum mechanical states representingcharge 1 quantum vortices/anti-vortices can be expressed as linearcombinations of single magnon states, composite multi-magnon states andthe ground state. Detailed calculations show that these states are quantummechanically stable states of the Hamiltonian provided that the systemsize exceeds certain threshold value. I will further argue that theinteractions between different magnon modes or rather fragile magnon modescan very well generate these topological excitations. Plausibility of ourcalculations in the real magnetic systems shall also be discussed.
