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Phase Transition of the S=1/2 Quantum Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice

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We study the S=1/2 anisotropic Heisenberg antiferromagnet on finite triangular lattices with N≤24 sites : H=2JΣ_<<i, j>>(S^x_i S^x_j+S^y_i S^y_j+ΔS^z_i S^z_j) with 0≤Δ≤1. The specific heat C and the chiral-order parameter <X^2> are calculated using a quantum transfer Monte Carlo method. Remarkable differences in the size dependences of C and <X^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 <X^2> to the thermodynamic limit gives a finite, non-zero value at low temperatures. In contrast with these, for Δ≥0.6, the peak height does not increase and the extrapolation of <X^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, non-zero temperature when Δ≤Δ_c with Δ_c≳0.4.

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