1203.6583 (Solomon A. Owerre)

Spin Wave Theory of Spin 1/2 XY Model with Ring Exchange on a Triangular
Lattice    [PDF]

Solomon A. Owerre

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson model (XY model) with nearest neighbour exchange $J$ and four-particle ring-exchange $K$ at half filling on the triangular lattice, and the phase diagrams of the system at zero and finite temperature. At zero temperature we find that the uniform superfluid phase in the pure $J$-model is quickly destroyed by the inclusion of a negative-$K$ ring-exchange interactions, favouring a state with a $(\frac{4\pi}{3}, 0)$ ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz-Thouless phase transition in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. Away from the pure $J$ point (pure XY model), $T_{KT}$ decreases rapidly for negative $K$, while for positive $K$, $T_{KT}$ reaches a maximum at some $K\neq 0$ in agreement with quantum Monte Carlo simulations in 2D model.

View original: http://arxiv.org/abs/1203.6583