Direct calculation of the spin stiffness of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on square, triangular, and cubic lattices using the coupled-cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled-cluster method. For the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on square, triangular, and cubic lattices, we calculate the stiffness in high orders of approximation. For square and cubic lattices, our results are in very good agreement with the best results available in the literature. For the triangular lattice, our result is more precise than any other result obtained thus far by other approximate method.

Figure 1

Illustration of the twisted Néel state: (a) square lattice and (b) triangular lattice. The twist is introduced along rows in the $x$ direction. The angles at the lattice sites indicated the twist of the spins with respect to the corresponding Néel state.

Figure 2

Extrapolation of the $\mathrm{CCM}\text{−}\mathrm{LSUB}n$ results for the stiffness. The points represent the $\mathrm{CCM}\text{−}\mathrm{LUB}n$ results, and the lines correspond to the function (8) fitted to these data points.