Microscopic calculation of the spin-stiffness constant for the spin-(1/2 square-lattice Heisenberg antiferromagnet

We discuss a systematic, microscopic calculation of the spin-stiffness constant ${\rho }_s$ for the spin-(1/2 square-lattice Heisenberg antiferromagnet. An infinitesimal twist is imposed upon the system by gradually rotating the direction of antiferromagnetic ordering. The difference in the ground-state energy of this system with respect to the uniformly ordered ground state can be related to the spin-stiffness constant ${\rho }_s$. Series expansions and extrapolation for the energy of the twisted system lead to the estimate &(=4${\mathrm{\rho }}_{\mathrm{s}}$/J)=0.72±0.0. The ratio of the series for ${\rho }_s$ and perpendicular susceptibility ${\chi }_{\perp }$ leads to an estimate for the spin-wave &(=${\mathrm{c}}_{\mathrm{s}}$/ √2 J)=1.18±0.02. The experiments on ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ are quantitatively consistent with a nearest-neighbor Heisenberg model when one takes into account these quantum renormalizations.