Study of the spin-phonon coupling in the antiferromagnetic Heisenberg three-leg ladder

The properties of spin-Peierls systems have been studied extensively since their discovery in 1975. In this thesis; we studied the spin-Peierls instability in the three-leg Heisenberg ladder coupled to phonons. The spin-½ antiferromagnetic Heisenberg three-leg ladder coupled to phonons is studied using the generalized Jordan-Wigner (JW) transformation and the bond-mean-field theory approach of Azzouz [1]. The free energy was calculated by mapping the spin operators of the Heisenberg Hamiltonian onto spinless JW fermions. The fermion interaction terms were treated within the framework of the bond-mean-field theory.; For the first time, we predict the spin-Peierls instability in the three-leg Heisenberg ladder. We support this key result of our theory by an analysis of the dependencies of the dimerization parameter delta vs the spin-phonon coupling constant lambda, the energy gap vs lambda, the energy gap vs temperature T and the spin-Peierls transition temperature TSP vs lambda with different values of the rung coupling alpha.