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

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

1994-10-25

arxiv.org/abs/cond-mat/9410090v1

Physics

Condensed Matter

4 pages, uuencoded compressed ps-file (made with uufiles)

Scientific paper

10.1103/PhysRevB.51.6151

We calculate the spin stiffness $\rho_s$ 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 $\rho_s = (0.183\pm 0.003)J_1$, 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 N\'eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N\'eel-ordered region.

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