Phase transition of theS=1/2 quantum anisotropic Heisenberg antiferromagnet on the triangular lattice

We study the S=1/2 anisotropic Heisenberg antiferromagnet on finite triangular lattices with N≤24 sites: H=2J${\mathcal{J}}_{\mathrm{〈}\mathit{i},}$ ${\mathit{j}}_{\mathrm{〉}}$(${\mathit{S}}_{\mathit{i}}^{\mathit{x}}$ ${\mathit{S}}_{\mathit{j}}^{\mathit{x}}$ +${\mathit{S}}_{\mathit{i}}^{\mathit{y}}$ ${\mathit{S}}_{\mathit{j}}^{\mathit{y}}$ +Δ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$) with 0≤Δ≤1. The specific heat C and the chiral-order parameter 〈${\mathrm{\chi }}^2$〉 are calculated using a quantum transfer Monte Carlo method. Remarkable differences in the size dependences of C and 〈${\mathrm{\chi }}^2$〉 are found between the cases of Δ≤0.4 and of Δ≥0.6. For Δ≤0.4, the peak height of C increases with increasing N and an extrapolation of 〈${\mathrm{\chi }}^2$〉 to the thermodynamic limit gives a finite, nonzero value at low temperatures. In contrast with these, for Δ≥0.6, the peak height does not increase and the extrapolation of 〈${\mathrm{\chi }}^2$〉 gives a smaller value even at very low temperatures indicating the absence of a long-range chiral order. From the results, we suggest that the chiral-ordered phase transition occurs at a finite, nonzero temperature when Δ≤${\mathrm{\Delta }}_{\mathit{c}}$ with ${\mathrm{\Delta }}_{\mathit{c}}$≳0.4. The phase diagram of the model is predicted.