Low-Energy Singlets in the Heisenberg Antiferromagnet on the Kagome Lattice

The spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the kagome lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic $T^2$ specific heat observed experimentally.

Figure 1

CORE on the kagome lattice (solid circles). Triangular blocks of first (second) CORE steps are encircled by solid (dashed) lines. On the right: triangle four ground states are labeled by spin (arrows) and pseudospins (wide arrows). The $\uparrow \Uparrow$ state of the triangle is visualized as a dimer singlet on the bottom rung.

Figure 2

CORE range 2. Directions of anisotropy vectors ${\mathbf{e}}_{ij}={\mathbf{e}}_{ij}^l={\tilde{\mathbf{e}}}_{ij}$ for a horizontal bond. For other bond directions, vectors must be rotated by $\pm 120°$. The ground state singlet correlations of two coupled blocks are depicted by thick lines.

Figure 3

Variational states on the triangular superlattice: The 3SL and the CD state; arrows denote pseudospins, and thick lines denote singlet dimers.

Figure 4

Clock fields $\varphi (\mathbf{x})$ (thick arrows) defined by the dimer directions from the sites marked by large circles.