Spin stiffness calculation in anisotropic XY model with Ring exchange interaction

الأصل · EN

We present the spin wave theory of XY model with anisotropic nearest neighbour (NN) interactions J(J′) along the x(y) directions, next nearest (NNN) neighbour interaction JD and the ring exchange interaction K on the square lattice. We calculate the thermodynamic quantities: Zero temperature spin stiffness, internal energy, specific heat and the magnetization. Using the diagonalized Hamiltonian, we show that no soft modes develop when η+ λ>0, where η= J′/J and λ= K/J. We further show that anisotropy (η=2) decreases the spin stiffness by 5.7% of its isotropic (η=1) maximum value for some values of λ and δ= JD/J. A similar reduction shows up in the magnetization. The plot of the stiffness against η(λ) reaches a maximum at η=0(λ=0) for specific values of δ and decreases rapidly as it approaches η+ λ+ 1=0. In general, the supersolid phase transition suggested earlierH will occur in the regime η+ λ+1 <0.