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Direct Calculation of the Spin Stiffness in the $J_1$--$J_2$ Heisenberg Antiferromagnet

T. Einarsson·H. J. Schulz
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Abstract

We calculate the spin stiffness $ρ_s$ for the frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a square lattice by exact diagonalizations on finite clusters of up to $36$ sites followed by extrapolations to the thermodynamic limit. For the non-frustrated case, we find that $ρ_s = (0.183\pm 0.003)J_1$, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for $0.4 \lesssim J_2/J_1 \lesssim 0.6$. In this intermediate region, the finite-size scaling works poorly -- an additional sign that their is neither Néel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the Néel-ordered region.

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T. Einarsson, H. J. Schulz. 1994-10-25. Direct Calculation of the Spin Stiffness in the $J_1$--$J_2$ Heisenberg Antiferromagnet. https://doi.org/10.1103/physrevb.51.6151

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