Entanglemend and Topological Soliton Structures in Heisenberg Spin Models

Abstract

Quantum entanglement and topological soliton characteristics of spin models are studied. By identifying spin states with qubits as a unit of quantum information, quantum information characteristic as entanglement is considered in terms of concurrence. Eigenvalues, eigenstates, density matrix and concurrence of two qubit Hamiltonian of XY Z, pure DM, Ising, XY , XX, XXX and XXZ models with Dzialoshinskii- Moriya DM interaction are constructed. For time evolution of two qubit states, periodic and quasiperiodic evolution of entanglement are found. Entangled two qubit states with exchange interaction depending on distance J(R) between spins and influence of this distance on entanglement of the system are considered. Different exchange interactions in the form of Calogero- Moser type I, II, III and Herring-Flicker potential which applicable to interaction of Hydrogen molecule are used. For geometric quantum computations, the geometric (Berry) phase in a two qubit XX model under the DM interaction in an applied magnetic field is calculated. Classical topological spin model in continuum media under holomorphic reduction is studied and static N soliton and soliton lattice configurations are constructed. The holomorphic time dependent Schrödinger equation for description of evolution in Ishimori model is derived. The influence of harmonic potential and bound state of solitons are studied. Relation of integrable soliton dynamics with multi particle problem of Calogero-Moser type is established and N soliton and N soliton lattice motion are found. Special reduction of Abelian Chern-Simons theory to complex Burgers. hierarchy, the Galilean group, dynamical symmetry and Negative Burgers. hierarchy are found.