Yangian symmetry in molecule V6 and four-spin Heisenberg model
Abstract
The symmetry operator Q=Y2 is introduced to re-describe the Heisenberg spin triangles in the \V6\ molecule, where Y stands for the Yangian operator which can be viewed as special form of Dzyaloshiky-Moriya (DM) interaction for spin 1/2 systems. Suppose a parallelogram Heisenberg model that is comprised of four 1/2-spins commutes with Q, which means that it possesses Yangian symmetry, we show that the ground state of the Hamiltonian H4 for the model allows to take the total spin S=1 by choosing some suitable exchange constants in H4. In analogy to the molecular \V6\ where the two triangles interact through Yangian operator we then give the magnetization for the theoretical molecule "\V8\" model which is comprised of two parallelograms. Following the example of molecule \V15\, we give another theoretical molecule model regarding the four 1/2-spins system with total spin S=1 and predict the local moments to be 1/10uB, 9/10uB, 1/10uB,9/10uB respectively.