1208.5089 (Solomon A. Owerre)

Effects of Dzyaloshinskii-Moriya interaction on Spin 1/2 XY Model with
Ring Exchange on a Triangular Lattice    [PDF]

Solomon A. Owerre

We analyse the linear spin wave theory calculation of the superfluid phase of a hard-core boson model with nearest neighbour exchange interaction $J$, Dzyaloshinskii-Moriya (DM) exchange interaction $D$ and four-particle ring-exchange interaction $K$ at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. We find that the DM interaction can be removed from the Hamiltonian by redefining the spin operators but this leads to a change in the nearest neighbour exchange interaction. We also find that the pure $J$ model (XY model) which has a well known uniform superfluid phase with an ordered parameter $< S_i^x>\neq 0$ at zero temperature is quickly destroyed by the inclusion of a negative-$K$ ring-exchange interactions for $D\neq0$, favouring a state with a $(\frac{4\pi}{3}, 0)$ ordering wavevector. We further study the behaviour of the zero temperature superfluid density and finite-temperature Kosterlitz-Thouless phase transition ($T_{KT}$) in the uniform superfluid phase for some values of $\kappa=K/J, \eta = D/J$, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. At zero temperature, we find that the maximum values of the superfluid density as a function of $\kappa$ increases as $\eta$ increases which shows that the DM exchange interaction constant increases the zero temperature superfluid density.

View original: http://arxiv.org/abs/1208.5089