Continuous-time worm quantum Monte Carlo study of a two-dimensional spin-one XXZ model

The spin models in condensed matter physics are important since the strong interaction between spins creates various quantum phases of interest. In this work, we explore the quantum critical region of a spin-one ( \(S=1\) $S=1$ ) quantum XXZ model in two dimensions. By adopting a worm algorithm proposed recently, we performed quantum Monte Carlo simulations in the parameter space of temperature (T) and the interaction strength of the z-directional spin component of nearest neighbor spins ( \(\Delta \) $\mathrm{\Delta }$ ). The phase diagram is obtained by comparing the Monte Carlo data and analytic consideration of superfluid stiffness and compressibility. We find the critical temperatures between the XY phase and the parameter phase by measuring the superfluid stiffness as a function of temperature and the critical strength of antiferromagnetic interaction ( \(\Delta _c\) ${\mathrm{\Delta }}_c$ ) by measuring the compressibility as a function of the strength of antiferromagnetic interaction. We compare the results with the case of \(S=\frac{1}{2}\) $S=\frac{1}{2}$ in our previous stochastic series expansion quantum Monte Carlo study.