Phase transition of theS=1/2 quantum anisotropic Heisenberg antiferromagnet on the triangular lattice
Naoki Suzuki, Fumitaka Matsubara
We study the S=1/2 anisotropic Heisenberg antiferromagnet on finite triangular lattices with N\ensuremath{\le}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}}$${\mathit{S}}_{\mathit{j}}^{\mathit{y}}$ +\ensuremath{\Delta}${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$) with 0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1. The specific heat C and the chiral-order parameter 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 are calculated using a quantum transfer Monte Carlo method. Remarkable differences in the size dependences of C and 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 are found between the cases of \ensuremath{\Delta}\ensuremath{\le}0.4 and of \ensuremath{\Delta}\ensuremath{\ge}0.6. For \ensuremath{\Delta}\ensuremath{\le}0.4, the peak height of C increases with increasing N and an extrapolation of 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 to the thermodynamic limit gives a finite, nonzero value at low temperatures. In contrast with these, for \ensuremath{\Delta}\ensuremath{\ge}0.6, the peak height does not increase and the extrapolation of 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 gives a smaller value even at very low temperatures indicating the absence of a long-range chiral order. From the results, we suggest that the chiral-ordered phase transition occurs at a finite, nonzero temperature when \ensuremath{\Delta}\ensuremath{\le}${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$ with ${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$\ensuremath{\gtrsim}0.4. The phase diagram of the model is predicted.
Physical review. B, Condensed matter•Mar 1, 1995•8 citations