Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice

We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization, and a variational mean-field approach. We find evidence that the star lattice is (besides the kagomé lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star lattice exhibits a huge nontrivial degeneracy like on the kagomé lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.

Figure 1

The star lattic with $N=42$ sites.

Figure 2

(Color online) Two variants of the GS of the classical HAFM on the star lattice: the $\sqrt{3}\times \sqrt{3}$ state (left) and the $q=0$ state (right). The dotted ellipses show further degrees of freedom of the highly degenerate classical GS. Different shades of the triangles symbolize different chiralities.

Figure 3

Maximal spin-spin correlation ${\mid ⟨{\widehat{S}}_0^z{\widehat{S}}_i^z⟩\mid }_{\max }$ versus separation $R=\mid {\mathbf{R}}_0-{\mathbf{R}}_i\mid$ for the star lattice $(N=42)$, the kagomé $(N=36)$, and the triangular lattice $(N=36)$ (the lines are guides for the eyes). The data for the kagomé lattice coincide with those from Ref. 20.

Figure 4

Low-energy spectrum for the HAFM on the star lattice $(N=36\mathrm{B})$ (the inset shows the $\mathbf{k}$ points in the Brillouin zone).

Figure 5

Finite-size behavior of the spin gap $\mathrm{\Delta }$, i.e., the gap to $s=1$ excitations versus inverse system size $1∕N$. Results are shown for the star lattice (triangles) in comparison with those for the kagomé lattice (circles, compare Ref. 23) and the triangular lattice (squares).

Figure 6

Magnetization curves for star lattices with $N=18$, 36A, and 36B (complete) and $N=42$, 54, and 72 (partial). Inset: High-field part of the magnetization curves for $N=36\mathrm{A}$, 36B, 54, and 72 sites.