Direct calculation of the spin stiffness in the ${\mathit{J}}_1$-${\mathit{J}}_2$ Heisenberg antiferromagnet

We calculate the spin stiffness ${\mathrm{\rho }}_{\mathit{s}}$ for the frustrated spin-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 nonfrustrated case, we find that ${\mathrm{\rho }}_{\mathit{s}}$=(0.183±0.003)${\mathit{J}}_1$, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for 0.4≲${\mathit{J}}_2$/${\mathit{J}}_1$≲0.6. In this intermediate region, the finite-size scaling works poorly—an additional sign that there 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.