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

Abstract

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson $J$-$K$ model with nearest neighbour exchange $J$ and four-particle ring-exchange $K$ 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 pure $J$ model (XY model) which has a well known uniform superfluid phase with an ordered parameter $M_x=<S_i^x>\ne 0$ at zero temperature 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 ($T_{KT}$) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for $K \textless 0$, the phase boundary monotonically decreases to T=0 at $K/J=-4/3$, where a phase transition is expected and $T_{KT}$ decreases rapidly while for positive $K$, $T_{KT}$ reaches a maximum at some $K\ne 0$. It has been shown on a square lattice using quantum Monte Carlo(QMC) simulations that for small $K\textgreater 0$ away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased\cite{F}. Our result seems to agree with this trend found in QMC simulations.

References in corpus (6)

• Supersolid hardcore bosons on the triangular lattice
• Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice
• Persistent supersolid phase of hard-core bosons on the triangular lattice
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Exotic phase diagram of a cluster charging model of bosons on the kagome lattice
• Superfluid and supersolid phases of lattice bosons with ring-exchange interaction

Cited by in corpus (4)

• $\text{Ab initio}$ theory of magnetism in two-dimensional $1T$-TaS${}_2$
• Haldane-like antiferromagnetic spin chain in the large anisotropy limit
• Berezinskii-Kosterlitz-Thouless Renormalization Group Flow at a Quantum Phase Transition
• Quantum-classical phase transition of the escape rate of two-sublattice antiferromagnetic large spins