Comparison of several tetrahedra-based lattices

A comparison of the quantum Heisenberg antiferromagnetic model (QHAM) on the pyrochlore lattice, the checkerboard lattice and the square lattice with crossing interactions is performed. The three lattices are constructed with the same tetrahedral unit cell and this property is used to describe the low energy spectrum by means of an effective hamiltonian restricted to the singlet sector. We analyze the structure of the effective hamiltonian and solve it within mean field approximation for the three lattices. 3 4 1 2 J J' (a) (b) (c) J J' Figure 1: Checkerboard (a), pyrochlore (b) and square lattice with crossing interactions. Bold lines represent intra-TT (J) interactions treated exactly, and thin lines represent inter-TT (J') interactions considered as a perturbation.