Series studies of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet at $T=0$: Magnon dispersion and structure factors

We have extended our previous series studies of quantum antiferromagnets at zero temperature by computing the one-magnon dispersion curves and various structure factors for the linear chain, square, and simple cubic lattices. Many of these results are a substantial extension of previous work. These results are directly comparable to neutron-scattering experiments, and we make such comparisons where possible.

Figure 1

The total and longitudinal structure factor for the linear chain.

Figure 2

(Color online) The one-magnon excitation spectrum $ϵ\left(\mathbf{k}\right)$ along high-symmetry cuts through the Brillouin zone for the Heisenberg antiferromagnet on a square lattice. Also shown are the results of first-order (blue dotted line), second-order (red dashed line), and third-order (green solid line) spin-wave theory.

Figure 3

(Color online) The various integrated structure factors $S_{\mathrm{tot}}$ (unpolarized), $S_{\mathrm{t}}$ (transverse), and $S_{\mathrm{l}}$ (longitudinal) along high-symmetry cuts through the Brillouin zone for the Heisenberg antiferromagnet on a square lattice.

Figure 4

(Color online) The one-magnon spectral weight $A_1$, and multimagnon spectral weights $W_{\mathrm{t}}$ and $W_{\mathrm{tot}}$ for the Heisenberg antiferromagnet on a square lattice.

Figure 5

(Color online) Ratio of longitudinal and transverse structure factors $2S_{\mathrm{l}}∕S_{\mathrm{t}}$ for the Heisenberg antiferromagnet on a square lattice. Also shown, for comparison, are the QMC results (Ref. 20).

Figure 6

(Color online) The one-magnon excitation spectrum $ϵ\left(\mathbf{k}\right)$ along high-symmetry cuts through the Brillouin zone for the Heisenberg antiferromagnet on the simple cubic lattice. Also shown are the results of first-order (blue dotted line) and second-order (red dashed line) spin-wave theory.

Figure 7

(Color online) The various integrated structure factors $S_{\mathrm{tot}}$ (unpolarized), $S_{\mathrm{t}}$ (transverse), and $S_{\mathrm{l}}$ (longitudinal) along high-symmetry cuts through the Brillouin zone for the Heisenberg antiferromagnet on a simple cubic lattice.

Figure 8

(Color online) The one-magnon spectral weight $A_1$, and multimagnon spectral weights $W_{\mathrm{t}}$ and $W_{\mathrm{tot}}$ for the Heisenberg antiferromagnet on the simple cubic lattice.

Figure 9

Ratio of longitudinal and transverse structure factors $2S_{\mathrm{l}}∕S_{\mathrm{t}}$ for the Heisenberg antiferromagnet on the simple cubic lattice.

Figure 10

(Color online) Comparison of the one-magnon dispersion for ${\mathrm{CFTD}}^3$ (red solid points) and our series results with $J=6.13\mathrm{meV}$.

Figure 11

(Color online) Comparison of the one-magnon transverse structure factor $A_1\left(\mathbf{k}\right)$ for ${\mathrm{CFTD}}^3$ (red solid points) and our series results.

Figure 12

Comparison of the one-magnon dispersion for ${\mathrm{Sr}}_2{\mathrm{Cu}}_3{\mathrm{O}}_4\mathrm{Cl}_2{}^4$ and our series results with $J=10.5\mathrm{meV}$, $\lambda =0.976$.